{"check_arguments":{"unspecified":[],"unsupported":[]},"citations":[{"citingPaper":{"authors":[{"authorId":"2435618378","name":"Madhur Mangalam"}],"citationStyles":{"bibtex":"@Inproceedings{Mangalam2026MarrsG,\n author = {Madhur Mangalam},\n booktitle = {Neuroscience &amp; Biobehavioral Reviews},\n title = {Marr\u2019s ghost},\n year = {2026}\n}\n"},"paperId":"ee3ffd9a3180e6b944f828b71eb8d9c066458acf","title":"Marr\u2019s ghost","venue":"Neuroscience &amp; Biobehavioral Reviews","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2375385056","name":"Suzanne Boyd"},{"authorId":"2262445895","name":"Christian Wolf"}],"citationStyles":{"bibtex":"@Inproceedings{Boyd2026ComputabilityPO,\n author = {Suzanne Boyd and Christian Wolf},\n title = {Computability properties of hyperbolic complex H\\'{e}non maps},\n year = {2026}\n}\n"},"paperId":"ed0c1353a951a65cb0ef362060c3820e6b93fa45","title":"Computability properties of hyperbolic complex H\\'{e}non maps","venue":"","year":2026},"contexts":["For further details, see subsection 2.1 and [54, 56]."]},{"citingPaper":{"authors":[{"authorId":"2349076043","name":"Shue Tian"},{"authorId":"2302332408","name":"Jiaqi Hu"},{"authorId":"2350914116","name":"Rebing Wu"},{"authorId":"2272324834","name":"Yu Shi"}],"citationStyles":{"bibtex":"@Inproceedings{Tian2026TrainingFreeQG,\n author = {Shue Tian and Jiaqi Hu and Rebing Wu and Yu Shi},\n title = {Training-Free Quantum Generative Paradigm via Local Parent Hamiltonians},\n year = {2026}\n}\n"},"paperId":"f0e2f4a8e1509c8b8ac3342761c7a76f6136af8e","title":"Training-Free Quantum Generative Paradigm via Local Parent Hamiltonians","venue":"","year":2026},"contexts":["Classical computability is grounded in the Turing machine formalism, which describes the forward computational process: given a well-defined set of rules M and an input x , compute the corresponding output y = M ( x ) [12]."]},{"citingPaper":{"authors":[{"authorId":"40451056","name":"Mathieu Hemery"}],"citationStyles":{"bibtex":"@Inproceedings{Hemery2026OnTD,\n author = {Mathieu Hemery},\n title = {On the Design of an Analog-Dyadic Converter CRN},\n year = {2026}\n}\n"},"paperId":"e063fb0aefd1260947f026202eb8b554ffbcd525","title":"On the Design of an Analog-Dyadic Converter CRN","venue":"","year":2026},"contexts":["A computer being any machine able to perform calculations [14]."]},{"citingPaper":{"authors":[{"authorId":"2322441318","name":"Krzysztof Olejniczak"},{"authorId":"2074443590","name":"Radoslav Dimitrov"},{"authorId":"2152662727","name":"Xingyue Huang"},{"authorId":"2288704253","name":"Bernardo Cuenca Grau"},{"authorId":"2280929245","name":"Jinwoo Kim"},{"authorId":"1810852785","name":".Ismail .Ilkan Ceylan"}],"citationStyles":{"bibtex":"@Inproceedings{Olejniczak2026WhatAT,\n author = {Krzysztof Olejniczak and Radoslav Dimitrov and Xingyue Huang and Bernardo Cuenca Grau and Jinwoo Kim and .Ismail .Ilkan Ceylan},\n title = {What are the Right Symmetries for Formal Theorem Proving?},\n year = {2026}\n}\n"},"paperId":"7feeb5ca61b2ae2a655c31011b2d97ba4b2d6628","title":"What are the Right Symmetries for Formal Theorem Proving?","venue":"","year":2026},"contexts":["Unfortunately, these are largely undecidable [58, 59]."]},{"citingPaper":{"authors":[{"authorId":"2361677209","name":"Ming Zhang"},{"authorId":"2372425057","name":"Qiyuan Peng"},{"authorId":"2354942636","name":"Yinxia Wei"},{"authorId":"2281737654","name":"Yujiong Shen"},{"authorId":"2400502336","name":"Kexin Tan"},{"authorId":null,"name":"Yuhui Wang"},{"authorId":"2288921730","name":"Zhen Xiang"},{"authorId":"2267498972","name":"Junjie Ye"},{"authorId":"2155273086","name":"Zhangyue Yin"},{"authorId":"2218237934","name":"Zhiheng Xi"},{"authorId":"2042683163","name":"Shihan Dou"},{"authorId":"2352016379","name":"Tao Gui"},{"authorId":"2438614046","name":"Maxm Pan"},{"authorId":"2322525492","name":"Rui Yang"},{"authorId":"2257376355","name":"Qi Zhang"},{"authorId":"2257129989","name":"Xuanjing Huang"}],"citationStyles":{"bibtex":"@Inproceedings{Zhang2026LLMEvalLogicAS,\n author = {Ming Zhang and Qiyuan Peng and Yinxia Wei and Yujiong Shen and Kexin Tan and Yuhui Wang and Zhen Xiang and Junjie Ye and Zhangyue Yin and Zhiheng Xi and Shihan Dou and Tao Gui and Maxm Pan and Rui Yang and Qi Zhang and Xuanjing Huang},\n title = {LLMEval-Logic: A Solver-Verified Chinese Benchmark for Logical Reasoning of LLMs with Adversarial Hardening},\n year = {2026}\n}\n"},"paperId":"d1076e8ef4a6b315a776043609a7d4a44fbdb5fc","title":"LLMEval-Logic: A Solver-Verified Chinese Benchmark for Logical Reasoning of LLMs with Adversarial Hardening","venue":"","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2151792079","name":"Guanyu Cui"},{"authorId":"2323902598","name":"Zhewei Wei"},{"authorId":"49810495","name":"Xiaosen Wang"}],"citationStyles":{"bibtex":"@Inproceedings{Cui2026PositionTT,\n author = {Guanyu Cui and Zhewei Wei and Xiaosen Wang},\n title = {Position: The Turing-Completeness of Autoregressive Transformers Relies Heavily on Context Management},\n year = {2026}\n}\n"},"paperId":"1a53559caa7da47580f5e10e741bd1dfb720e944","title":"Position: The Turing-Completeness of Autoregressive Transformers Relies Heavily on Context Management","venue":"","year":2026},"contexts":["Turing machines (TMs) are a classical computational model proposed by Alan Turing (Turing, 1937) to formalize the notion of computability."]},{"citingPaper":{"authors":[{"authorId":"2383169506","name":"Milan Rosko"}],"citationStyles":{"bibtex":"@Inproceedings{Rosko2026RemarksOP,\n author = {Milan Rosko},\n title = {Remarks on Primitive Regulation},\n year = {2026}\n}\n"},"paperId":"6feb95f9084e5d645942efd4e738f5d406e3fa26","title":"Remarks on Primitive Regulation","venue":"","year":2026},"contexts":["\u2026of syntax; Undefinability [Tarski, 1933] proceeds by diagonalizing against a hypothesized truth predicate; Semidecid-ability [Church, 1936; Turing, 1937; Kleene, 1952; Rice, 1953] presupposes a fixed model of computation; L\u00f6b\u2019s Theorem [L\u00f6b, 1955] depends on the modal derivability\u2026"]},{"citingPaper":{"authors":[{"authorId":"2138209475","name":"M. Ruban"}],"citationStyles":{"bibtex":"@Inproceedings{Ruban2026TheEH,\n author = {M. Ruban},\n booktitle = {Studies in history and philosophy of science and technology},\n title = {The ethical horizon of the Technosphere: a holistic chain of responsibility of the cognitive agent in eastern European twentieth-century science fiction},\n year = {2026}\n}\n"},"paperId":"76716eb68448a908b2044357bd9252beda692801","title":"The ethical horizon of the Technosphere: a holistic chain of responsibility of the cognitive agent in eastern European twentieth-century science fiction","venue":"Studies in history and philosophy of science and technology","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2064335424","name":"Ezequiel L\u00f3pez-Rubio"}],"citationStyles":{"bibtex":"@Inproceedings{L\u00f3pez-Rubio2026TheIP,\n author = {Ezequiel L\u00f3pez-Rubio},\n title = {The IsalProgram Programming Language},\n year = {2026}\n}\n"},"paperId":"ecea5bfca9e8e171b169a54b50a79388d6e1a084","title":"The IsalProgram Programming Language","venue":"","year":2026},"contexts":["Standard computability arguments are developed with respect to Turing machines [Turing, 1936, Sipser, 2012].","We simulate a two-tape Turing machine (TM) [Turing, 1936, Minsky, 1967].","As with all Turing-complete languages, the halting problem for IsalProgram is undecidable [Turing, 1936].","Despite its syntactic minimality, IsalProgram is computationally universal: we show in Section 6 that it can simulate a Turing machine, placing it in the class of Turing-complete languages [Turing, 1936, Sipser, 2012]."]},{"citingPaper":{"authors":[{"authorId":"115310207","name":"Juan A. Cabrera"},{"authorId":"2180423601","name":"Pit Hofmann"},{"authorId":"2220363210","name":"Jonas Schulz"},{"authorId":"2375928700","name":"Frederic Benken"},{"authorId":"47068255","name":"Hrjehor Mark"},{"authorId":"2298072178","name":"Giang T. Nguyen"},{"authorId":"2372390466","name":"Holger Boche"},{"authorId":"2270255398","name":"Frank H. P. Fitzek"}],"citationStyles":{"bibtex":"@Inproceedings{Cabrera2026TheSP,\n author = {Juan A. Cabrera and Pit Hofmann and Jonas Schulz and Frederic Benken and Hrjehor Mark and Giang T. Nguyen and Holger Boche and Frank H. P. Fitzek},\n title = {The Shared Prosperity Internet},\n year = {2026}\n}\n"},"paperId":"14652fda84d98036e53fafa783e7ab4e58b76356","title":"The Shared Prosperity Internet","venue":"","year":2026},"contexts":["The ideal digital computer is the Turing machine [9], i.e., a machine capable of computing any computable function."]},{"citingPaper":{"authors":[{"authorId":"102221212","name":"B. Wardhaugh"}],"citationStyles":{"bibtex":"@Inproceedings{Wardhaugh2026AlgorithmicJL,\n author = {B. Wardhaugh},\n booktitle = {International Review of Law, Computers &amp; Technology},\n title = {Algorithmic judging: lessons of logic and jurisprudence},\n year = {2026}\n}\n"},"paperId":"9970a281f1c5369317f9086066d922be99173116","title":"Algorithmic judging: lessons of logic and jurisprudence","venue":"International Review of Law, Computers &amp; Technology","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2263414153","name":"K. Svozil"}],"citationStyles":{"bibtex":"@Inproceedings{Svozil2026ThePA,\n author = {K. Svozil},\n title = {The Physical and Contextual Limits of Quantum Speedup},\n year = {2026}\n}\n"},"paperId":"342ced3d0c2237f94e9fc95aba1ec56129dcbf8d","title":"The Physical and Contextual Limits of Quantum Speedup","venue":"","year":2026},"contexts":["It acts on symbolic inputs of arbitrary length, admits arbitrarily long compu-5 tations, supports parsing and composition of programs, and allows self-reference through coding of machines by strings [36, 37]."]},{"citingPaper":{"authors":[{"authorId":"2326812345","name":"Hongyu Chen"},{"authorId":"152617877","name":"James McGowan"},{"authorId":"2297884637","name":"Michael Franz"}],"citationStyles":{"bibtex":"@Inproceedings{Chen2026DeterministicFW,\n author = {Hongyu Chen and James McGowan and Michael Franz},\n title = {Deterministic Fully-Static Whole-Binary Translation without Heuristics},\n year = {2026}\n}\n"},"paperId":"72adb1fc366fc36a55e1d267c8bce81c4c397826","title":"Deterministic Fully-Static Whole-Binary Translation without Heuristics","venue":"","year":2026},"contexts":["As mentioned in Section 2, distinguishing code from data in a binary is in general equivalent to the Halting Problem [40] and therefore unsolvable; every static translator that attempts to commit, at each byte of the input, to a single interpretation is forced to rely on heuristics that will be\u2026","\u2026far back as 1980 that the general problem of \u201cdetranslating\u201d (decompiling/disassembling) a binary executable requires being able to differentiate with certainty between code and data, which for most computer architectures is equivalent to the Halting Problem [40] and is hence unsolvable in general."]},{"citingPaper":{"authors":[{"authorId":"2267377971","name":"Flavio Ferrarotti"},{"authorId":"2301278317","name":"Vincenzo Gervasi"},{"authorId":"1700774","name":"Alexander Raschke"},{"authorId":"1739884","name":"K. Schewe"}],"citationStyles":{"bibtex":"@Inproceedings{Ferrarotti2026TheAS,\n author = {Flavio Ferrarotti and Vincenzo Gervasi and Alexander Raschke and K. Schewe},\n booktitle = {Formal Aspects of Computing},\n title = {The Abstract State Machines Method},\n year = {2026}\n}\n"},"paperId":"5b27b4a6299695312d6432664d19c21fb0e2a633","title":"The Abstract State Machines Method","venue":"Formal Aspects of Computing","year":2026},"contexts":["This is a thesis, not a theorem, which in Turing\u2019s original work [168, 169] is motivated by assuming that a man doing a computation would only need paper, pencil and rubber, and work with strict discipline, thus act in efect just like a universal Turing machine."]},{"citingPaper":{"authors":[{"authorId":"2237425028","name":"Shekhar S. Chandra"}],"citationStyles":{"bibtex":"@Inproceedings{Chandra2026VonNN,\n author = {Shekhar S. Chandra},\n title = {Von Neumann Networks},\n year = {2026}\n}\n"},"paperId":"0c53ce623b02a3972ada6b124e692f489b23496c","title":"Von Neumann Networks","venue":"","year":2026},"contexts":["Alan Turing (Turing, 1937) introduced just such a machine in order to study the \u201cEntscheidungsproblem\u201d (or the decision problem) and in the process developed a theory of computation.","Alan Turing constructed the original universal Turing machine (UTM) as the first type (Turing, 1937) (see Appendix D for a basic introduction), Johnie introduced the Von Neumann (hardware) architecture as second type (von Neumann, 1993) and the GoL proof (Rendell, 2013) is example of the third type."]},{"citingPaper":{"authors":[{"authorId":"47261140","name":"Guangyan Zhou"},{"authorId":"2152593702","name":"Bin Wang"},{"authorId":"2293667864","name":"Jianxin Wang"},{"authorId":"2277694536","name":"Ke Xu"}],"citationStyles":{"bibtex":"@Inproceedings{Zhou2026SolutionIA,\n author = {Guangyan Zhou and Bin Wang and Jianxin Wang and Ke Xu},\n title = {Solution independence and self-referential instances},\n year = {2026}\n}\n"},"paperId":"7255ff7d32b24fe7d96686de5734512bcae165c3","title":"Solution independence and self-referential instances","venue":"","year":2026},"contexts":["Building upon these foundational ideas, Church [3] and Turing [9] extended the notion of self-reference and pioneered computability theory."]},{"citingPaper":{"authors":[{"authorId":"2316050616","name":"Marcus J Hamilton"},{"authorId":"2280177745","name":"Abhishek Yadav"},{"authorId":"2267294207","name":"Harrison Hartle"},{"authorId":"2145720225","name":"Jan Korbel"},{"authorId":"51210849","name":"Niels Kornerup"},{"authorId":"1466510389","name":"A. Stier"},{"authorId":"2285148770","name":"Douglas H. Erwin"},{"authorId":"2310970033","name":"Hyejin Youn"},{"authorId":"2359633841","name":"Christopher P. Kempes"},{"authorId":"40196302","name":"Hajime Shimao"},{"authorId":"2269815068","name":"Kyle Harper"},{"authorId":"2256979427","name":"James Evans"},{"authorId":"2296207294","name":"David H. Wolpert"}],"citationStyles":{"bibtex":"@Inproceedings{Hamilton2026ComputationalFO,\n author = {Marcus J Hamilton and Abhishek Yadav and Harrison Hartle and Jan Korbel and Niels Kornerup and A. Stier and Douglas H. Erwin and Hyejin Youn and Christopher P. Kempes and Hajime Shimao and Kyle Harper and James Evans and David H. Wolpert},\n title = {Computational foundations of the human world},\n year = {2026}\n}\n"},"paperId":"f5473a6745fb427f9ecb95d6941134a83a274d51","title":"Computational foundations of the human world","venue":"","year":2026},"contexts":["The Church-Turing thesis [105, 106] holds that a Turing Machine is a universal model of computation, meaning that it is theoretically capable of simulating any algorithm or computing device, thereby defining the absolute limits of what is computable."]},{"citingPaper":{"authors":[{"authorId":"153371603","name":"Takuma Imamura"}],"citationStyles":{"bibtex":"@Inproceedings{Imamura2026HallucinationAA,\n author = {Takuma Imamura},\n title = {Hallucination, abstention, and computable inseparability},\n year = {2026}\n}\n"},"paperId":"59630de842893dab7dc5b1522b1cd4da79f442aa","title":"Hallucination, abstention, and computable inseparability","venue":"","year":2026},"contexts":["This is just the usual undecidability argument, for example the halting problem, going back to the classical work of Church (1936); Turing (1937)."]},{"citingPaper":{"authors":[{"authorId":"2260283233","name":"Haofei Yu"},{"authorId":"2301218271","name":"Yining Zhao"},{"authorId":"40642563","name":"L. Blum"},{"authorId":"2058090710","name":"M. Blum"},{"authorId":"2347038445","name":"Paul Pu Liang"}],"citationStyles":{"bibtex":"@Inproceedings{Yu2026CTMAIAB,\n author = {Haofei Yu and Yining Zhao and L. Blum and M. Blum and Paul Pu Liang},\n title = {CTM-AI: A Blueprint for General AI Inspired by a Model of Consciousness},\n year = {2026}\n}\n"},"paperId":"ebf290a5b163c13ab656e06aa997c94e9536427d","title":"CTM-AI: A Blueprint for General AI Inspired by a Model of Consciousness","venue":"","year":2026},"contexts":["The CTM is a simple and formal model of consciousness (Blum & Blum, 2021; 2022) inspired by Alan Turing\u2019s model of computation (Turing, 1936) and Bernard Baars\u2019 theater model of consciousness (Baars, 1993).","The CTM is a simple and formal model of consciousness inspired by Alan Turing\u2019s model of computation (Turing, 1936) and Bernard Baars\u2019 theater model of consciousness (Baars, 1993)."]},{"citingPaper":{"authors":[{"authorId":"1387957937","name":"Andrew E. M. Lewis-Pye"},{"authorId":"2297770867","name":"Ehud Shapiro"}],"citationStyles":{"bibtex":"@Inproceedings{Lewis-Pye2026VolitionalMA,\n author = {Andrew E. M. Lewis-Pye and Ehud Shapiro},\n title = {Volitional Multiagent Atomic Transactions: Describing People and their Machines},\n year = {2026}\n}\n"},"paperId":"a0b4226bb914b3829ed1298c4f37949629acb6e6","title":"Volitional Multiagent Atomic Transactions: Describing People and their Machines","venue":"","year":2026},"contexts":["Before defining what we now call Turing machines (automatic machines, or a-machines), Turing [48] introduced choice machines (c-machines), \u201cwhose motion is only partially determined by the configuration\u201d\u2014at designated states, the machine \u201ccannot go on until some arbitrary choice has been made by an\u2026","Across all surveyed formal traditions\u2014Turing\u2019s choice machines [48], CSP [20], CCS [31], I/O automata [30], angelic/demonic nondeterminism [5], ATL [3], game semantics [1], ceremony analysis [16], electronic institutions [17]\u2014the person is modelled as environment, opponent, error source, or\u2026","Turing\u2019s choice machines [48] introduced the person as an external operator making free choices at designated states."]},{"citingPaper":{"authors":[{"authorId":"2315208451","name":"Y. Gunji"},{"authorId":"2393641359","name":"Kyoko Nakamura"},{"authorId":"34982450","name":"K. Sasai"},{"authorId":"34103812","name":"Iori Tani"},{"authorId":"2439134099","name":"Mayo Kuroki"},{"authorId":"2024714","name":"A. Chiolerio"},{"authorId":"2266929936","name":"Andrew Adamatzky"},{"authorId":"2258790999","name":"Andrei Yu. Khrennikov"}],"citationStyles":{"bibtex":"@Inproceedings{Gunji2026InterplayBV,\n author = {Y. Gunji and Kyoko Nakamura and K. Sasai and Iori Tani and Mayo Kuroki and A. Chiolerio and Andrew Adamatzky and Andrei Yu. Khrennikov},\n booktitle = {Entropy},\n title = {Interplay Between Vertical and Horizontal Schemes of Computation: From Bayesian Inference to Quantum Logic via Gluing Boolean Algebras},\n year = {2026}\n}\n"},"paperId":"667dd8e2800e95a79ab25590171bec985dbde8e7","title":"Interplay Between Vertical and Horizontal Schemes of Computation: From Bayesian Inference to Quantum Logic via Gluing Boolean Algebras","venue":"Entropy","year":2026},"contexts":["Such a system can be described by recursive functions [48\u201350] equivalent to Turing machines [51] or automata."]},{"citingPaper":{"authors":[{"authorId":"2144142273","name":"Yongquan Yang"}],"citationStyles":{"bibtex":"@Inproceedings{Yang2026NegativeOO,\n author = {Yongquan Yang},\n title = {Negative Ontology of True Target for Machine Learning: Towards Evaluation and Learning under Democratic Supervision},\n year = {2026}\n}\n"},"paperId":"53039f41a7b8c8870fa9abc3c8c38231848fc065","title":"Negative Ontology of True Target for Machine Learning: Towards Evaluation and Learning under Democratic Supervision","venue":"","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2012123587","name":"Somyajit Chakraborty"}],"citationStyles":{"bibtex":"@Inproceedings{Chakraborty2026ACT,\n author = {Somyajit Chakraborty},\n title = {A Co-Evolutionary Theory of Human-AI Coexistence: Mutualism, Governance, and Dynamics in Complex Societies},\n year = {2026}\n}\n"},"paperId":"8934c6ce891c73809b960699951a2fa08a263dd7","title":"A Co-Evolutionary Theory of Human-AI Coexistence: Mutualism, Governance, and Dynamics in Complex Societies","venue":"","year":2026},"contexts":["\u2026and early symbolic AI all portrayed the machine as an entity whose competence arose from explicit procedure, symbolic representation, and bounded state transition [Turing, 1937, Rabin and Scott, 1959, McCulloch and Pitts, 1943, Shannon, 1948, Wiener, 1948, Newell et al., 1956, McCarthy, 1959]."]},{"citingPaper":{"authors":[{"authorId":"2405807490","name":"Neil D. Lawrence"}],"citationStyles":{"bibtex":"@Inproceedings{Lawrence2026TheNB,\n author = {Neil D. Lawrence},\n title = {The No Barber Principle: Towards Formalised Selection in the Inaccessible Game},\n year = {2026}\n}\n"},"paperId":"35441ed80eaa3ef78538d4450b9c3493b8db0b9b","title":"The No Barber Principle: Towards Formalised Selection in the Inaccessible Game","venue":"","year":2026},"contexts":["Lawvere (1969) showed that Russell\u2019s barber paradox has a common category theoretic structure with other proofs including Cantor\u2019s theorem Cantor (1891), G\u00f6del incompleteness (G\u00f6del, 1931), Turing\u2019s halting problem (Turing, 1936), and Tarski\u2019s undefinability theorem (Tarski, 1936)."]},{"citingPaper":{"authors":[{"authorId":"2263414153","name":"K. Svozil"}],"citationStyles":{"bibtex":"@Inproceedings{Svozil2026AgainstAU,\n author = {K. Svozil},\n title = {Against a Universal Trading Strategy: No-Arbitrage, No-Free-Lunch, and Adversarial Cantor Diagonalization},\n year = {2026}\n}\n"},"paperId":"c948f1612d5d2b4bd0face6f23b8e69838928464","title":"Against a Universal Trading Strategy: No-Arbitrage, No-Free-Lunch, and Adversarial Cantor Diagonalization","venue":"","year":2026},"contexts":["Shifting the paradigm from exogenous price processes to adaptive environments, we utilize the core diag-onalization logic of the Halting Problem [7] to show that no computable strategy can survive an adversary capable of simulating it.","This guarantees its defeat via formal Turing diagonalization [7, 11]."]},{"citingPaper":{"authors":[{"authorId":"2328290453","name":"Jonathan Brossard"}],"citationStyles":{"bibtex":"@Inproceedings{Brossard2026ACP,\n author = {Jonathan Brossard},\n title = {A Constructive Proof of Rice's Theorem and the Halting Problem via Hilbert's Tenth Problem},\n year = {2026}\n}\n"},"paperId":"9532f6cb0e7895363e3a076c60f1451c60dccd60","title":"A Constructive Proof of Rice's Theorem and the Halting Problem via Hilbert's Tenth Problem","venue":"","year":2026},"contexts":["The halting problem [Tur36] is the most famous specific instance: no algo-rithm decides, for an arbitrary program and input, whether the program halts."]},{"citingPaper":{"authors":[{"authorId":"2274480799","name":"\u00c9ireann Leverett"},{"authorId":"2273645089","name":"Jeroen van der Ham-de Vos"}],"citationStyles":{"bibtex":"@Inproceedings{Leverett2026VulnerabilityAA,\n author = {\u00c9ireann Leverett and Jeroen van der Ham-de Vos},\n title = {Vulnerability Abundance: A formal proof of infinite vulnerabilities in code},\n year = {2026}\n}\n"},"paperId":"10bfec7512a7d869dc7b83d03292a13d741e5082","title":"Vulnerability Abundance: A formal proof of infinite vulnerabilities in code","venue":"","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2158832","name":"N. Janson"},{"authorId":"2375903455","name":"Adam E. Essex"},{"authorId":"2274254578","name":"A. G. Balanov"}],"citationStyles":{"bibtex":"@Inproceedings{Janson2026DesigningEC,\n author = {N. Janson and Adam E. Essex and A. G. Balanov},\n booktitle = {Physica A: Statistical Mechanics and its Applications},\n title = {Designing explainable cognitive systems and explaining neural networks with plastic dynamical systems},\n year = {2026}\n}\n"},"paperId":"662fc2bd583042740c33725e74ea5dd69568cc22","title":"Designing explainable cognitive systems and explaining neural networks with plastic dynamical systems","venue":"Physica A: Statistical Mechanics and its Applications","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2291994275","name":"Junjie Zhang"},{"authorId":"2238404540","name":"Zhen Shen"},{"authorId":"2348385356","name":"Gang Xiong"},{"authorId":"39083111","name":"Xisong Dong"}],"citationStyles":{"bibtex":"@Inproceedings{Zhang2026GrokkingFA,\n author = {Junjie Zhang and Zhen Shen and Gang Xiong and Xisong Dong},\n title = {Grokking From Abstraction to Intelligence},\n year = {2026}\n}\n"},"paperId":"76918122a493c52c9b70ae2c7bca5b3ddad21bc5","title":"Grokking From Abstraction to Intelligence","venue":"","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2317898031","name":"Boumediene Hamzi"},{"authorId":"2293720481","name":"Marianne Clausel"},{"authorId":"2373035324","name":"Kamal Dingle"},{"authorId":"2267490183","name":"Marcus Hutter"},{"authorId":"2212623253","name":"Mohammed Terry-Jack"}],"citationStyles":{"bibtex":"@Inproceedings{Hamzi2026TimeSC,\n author = {Boumediene Hamzi and Marianne Clausel and Kamal Dingle and Marcus Hutter and Mohammed Terry-Jack},\n title = {Time Series Correlations and Kolmogorov Complexity: A Hausdorff Dimension Perspective},\n year = {2026}\n}\n"},"paperId":"23f8efa373ac9fb7d765b4db0bd1e2fbd9339825","title":"Time Series Correlations and Kolmogorov Complexity: A Hausdorff Dimension Perspective","venue":"","year":2026},"contexts":["K ( x ) is more technically defined as the length of a shortest program which runs on an optimal prefix universal Turing machine (UTM) [10], generates x , and halts."]},{"citingPaper":{"authors":[{"authorId":"144363427","name":"G. Piccinini"}],"citationStyles":{"bibtex":"@Inproceedings{Piccinini2026AllocentricNI,\n author = {G. Piccinini},\n title = {Allocentric Navigation Is Computationally Universal},\n year = {2026}\n}\n"},"paperId":"1557924efac1c5e83a2b46ebe85656b6901cce9d","title":"Allocentric Navigation Is Computationally Universal","venue":"","year":2026},"contexts":["The benchmark is Turing universality in the standard sense established by Turing's analysis of effective calculability (Turing, 1937)."]},{"citingPaper":{"authors":[{"authorId":"2373757966","name":"Enrique Junquera"},{"authorId":"2354166231","name":"Carlos P\u00e9rez-Carrera"},{"authorId":"2337130975","name":"Higinio Rubio"},{"authorId":"153823875","name":"A. Bustos"}],"citationStyles":{"bibtex":"@Inproceedings{Junquera2026AdvancesTA,\n author = {Enrique Junquera and Carlos P\u00e9rez-Carrera and Higinio Rubio and A. Bustos},\n booktitle = {Electronics},\n title = {Advances, Trends and Challenges for Determining the Condition of Railway Rolling Stock Using Automatic Classifiers: A Systematic Review},\n year = {2026}\n}\n"},"paperId":"d6a8b1f75bc63b269a34bd034816b84a72e6f4ba","title":"Advances, Trends and Challenges for Determining the Condition of Railway Rolling Stock Using Automatic Classifiers: A Systematic Review","venue":"Electronics","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2257052321","name":"Cheng Yang"}],"citationStyles":{"bibtex":"@Inproceedings{Yang2026AJA,\n author = {Cheng Yang},\n title = {A Judge Agent Closes the Reliability Gap in AI-Generated Scientific Simulation},\n year = {2026}\n}\n"},"paperId":"6c378fc523dcf944113704a866635052714cceea","title":"A Judge Agent Closes the Reliability Gap in AI-Generated Scientific Simulation","venue":"","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"47234416","name":"D. Spennemann"}],"citationStyles":{"bibtex":"@Inproceedings{Spennemann2026WhatMB,\n author = {D. Spennemann},\n booktitle = {The Heritage},\n title = {What Might Be the Possible Conditions for Artificial Intelligence to Become Cultural Beings and to Develop a Cultural Heritage of Their Own?},\n year = {2026}\n}\n"},"paperId":"882a6397a7a593d2d467fdd38e019a763fd298e8","title":"What Might Be the Possible Conditions for Artificial Intelligence to Become Cultural Beings and to Develop a Cultural Heritage of Their Own?","venue":"The Heritage","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"52120693","name":"Oseni Taiwo Afisi"}],"citationStyles":{"bibtex":"@Inproceedings{Afisi2026TheIO,\n author = {Oseni Taiwo Afisi},\n booktitle = {Advanced Research Journal},\n title = {The interplay of philosophical logic and computer science: Foundations, logical connectives, and contemporary computational applications},\n year = {2026}\n}\n"},"paperId":"b0abf7e7252b80ee0919262e520b09ed8f1ed872","title":"The interplay of philosophical logic and computer science: Foundations, logical connectives, and contemporary computational applications","venue":"Advanced Research Journal","year":2026},"contexts":["Computation, in this classical view, was seen as derivative, as an application of logical principles rather than a factor capable of reshaping them (Church, 1936; Turing, 1936).","\u2026same time, Alonzo Church and Alan Mathison Turing independently developed formal models of computation\u2014the \u03bb-calculus and the Turing machine\u2014thereby establishing the theoretical foundations of computability and revealing deep connections between logic and computation (Church, 1936; Turing, 1936)."]},{"citingPaper":{"authors":[{"authorId":"2391905467","name":"Sibasish Mishra"},{"authorId":"2284863002","name":"Aritra Sarkar"},{"authorId":"2311506479","name":"Sebastian Feld"}],"citationStyles":{"bibtex":"@Inproceedings{Mishra2026EQISAEQ,\n author = {Sibasish Mishra and Aritra Sarkar and Sebastian Feld},\n title = {EQISA: Energy-efficient Quantum Instruction Set Architecture using Sparse Dictionary Learning},\n year = {2026}\n}\n"},"paperId":"f6110d0bf99ee300611212659ce8843817e03cd6","title":"EQISA: Energy-efficient Quantum Instruction Set Architecture using Sparse Dictionary Learning","venue":"","year":2026},"contexts":["This limitation arises because calculating the true Kolmogorov complexity entails solving the halting problem, which is undecidable [48]."]},{"citingPaper":{"authors":[{"authorId":"2294455116","name":"L. M. Lazi\u0107"}],"citationStyles":{"bibtex":"@Inproceedings{Lazi\u01072026ArtificialIA,\n author = {L. M. Lazi\u0107},\n booktitle = {2026 25th International Symposium INFOTEH-JAHORINA (INFOTEH)},\n title = {Artificial Intelligence and Personality: The Role of Personality Traits in Shaping Attitudes Toward Artificial Intelligence},\n year = {2026}\n}\n"},"paperId":"1beddea3ac45b998d37dba912b4b06fd5db54275","title":"Artificial Intelligence and Personality: The Role of Personality Traits in Shaping Attitudes Toward Artificial Intelligence","venue":"2026 25th International Symposium INFOTEH-JAHORINA (INFOTEH)","year":2026},"contexts":["In his work [4], he introduced the concept of universal machines, theoretical computer science, and an understanding of the limits of computability."]},{"citingPaper":{"authors":[{"authorId":"2064020098","name":"A. Schumann"}],"citationStyles":{"bibtex":"@Inproceedings{Schumann2026MyceliumAD,\n author = {A. Schumann},\n booktitle = {International Journal of Parallel, Emergent and Distributed Systems},\n title = {Mycelium as dynamic simplicial complexes: a topological framework for fungal computation},\n year = {2026}\n}\n"},"paperId":"547587fd88a5f4f363cc9595dcef511ef618618d","title":"Mycelium as dynamic simplicial complexes: a topological framework for fungal computation","venue":"International Journal of Parallel, Emergent and Distributed Systems","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2485738","name":"Romain Peyrichou"}],"citationStyles":{"bibtex":"@Inproceedings{Peyrichou2026TheGA,\n author = {Romain Peyrichou},\n title = {The Generation-Recognition Asymmetry: Six Dimensions of a Fundamental Divide in Formal Language Theory},\n year = {2026}\n}\n"},"paperId":"bd8017b6fbe29542ccd8d0ff02cc8ac8628523a1","title":"The Generation-Recognition Asymmetry: Six Dimensions of a Fundamental Divide in Formal Language Theory","venue":"","year":2026},"contexts":["For recursively enumerable languages ( k = 0), finally, the membership decision is undecidable [53] \u2014 an intrinsic tight characterization, equivalent to the halting problem.","Given an arbitrary semantic constraint C , deciding whether there exists w \u2208 L ( G ) satisfying C amounts to the halting problem [53]. n (constraint size or target string) The sign reversal of the asymmetry."]},{"citingPaper":{"authors":[{"authorId":"2246165308","name":"Serge Massar"}],"citationStyles":{"bibtex":"@Inproceedings{Massar2026ConsistencyOG,\n author = {Serge Massar},\n title = {Consistency of Generalised Probabilistic Theories is Undecidable},\n year = {2026}\n}\n"},"paperId":"9649e00ec4157d96b37b59b53cc50d1df7f8d094","title":"Consistency of Generalised Probabilistic Theories is Undecidable","venue":"","year":2026},"contexts":["Deciding such questions is as hard as deciding whether a Turing machine halts [23]."]},{"citingPaper":{"authors":[{"authorId":"2332997","name":"E. Jeandel"}],"citationStyles":{"bibtex":"@Inproceedings{Jeandel2026ACA,\n author = {E. Jeandel},\n booktitle = {Theoretical Computer Science},\n title = {A categorical approach to reversible Turing machines and Brin-Thompson groups},\n year = {2026}\n}\n"},"paperId":"0d6e9bcd955bb11bf83216d8041af8577277a42f","title":"A categorical approach to reversible Turing machines and Brin-Thompson groups","venue":"Theoretical Computer Science","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2257384570","name":"Florbela Gon\u00e7alves"},{"authorId":"2257389884","name":"Margarida Gaud\u00eancio"},{"authorId":"2392060343","name":"Sofia B. Nunes"},{"authorId":"2366359612","name":"Francisca Rego"},{"authorId":"2270199560","name":"R. Nunes"}],"citationStyles":{"bibtex":"@Inproceedings{Gon\u00e7alves2026ImpactOA,\n author = {Florbela Gon\u00e7alves and Margarida Gaud\u00eancio and Sofia B. Nunes and Francisca Rego and R. Nunes},\n booktitle = {Healthcare},\n title = {Impact of Artificial Intelligence on the Care of Terminally Ill Patients},\n year = {2026}\n}\n"},"paperId":"ddb4a67dd18a6bd1d65ce7adc3a6686d43e383bd","title":"Impact of Artificial Intelligence on the Care of Terminally Ill Patients","venue":"Healthcare","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"46204455","name":"Sahil Imtiyaz"}],"citationStyles":{"bibtex":"@Inproceedings{Imtiyaz2026ConstraintSF,\n author = {Sahil Imtiyaz},\n booktitle = {bioRxiv},\n title = {Constraint Semantics for Multi-level Organisation},\n year = {2026}\n}\n"},"paperId":"01592ada361f821aa3c00616b29629562eb16463","title":"Constraint Semantics for Multi-level Organisation","venue":"bioRxiv","year":2026},"contexts":["Fixed alphabet, fixed rule set, closed configuration space; semantics externally specified [64].","Turing machines, \u03bb -calculus, classical algorithms [8, 64] Computation as execution of a fixed program (transition/reduction rules) on configurations/terms [8, 64]."]},{"citingPaper":{"authors":[{"authorId":"2260901043","name":"V. Loreto"},{"authorId":"2776193","name":"V. Servedio"},{"authorId":"2583711","name":"F. Tria"}],"citationStyles":{"bibtex":"@Inproceedings{Loreto2026TheSO,\n author = {V. Loreto and V. Servedio and F. Tria},\n title = {The Science of the New},\n year = {2026}\n}\n"},"paperId":"407dc9bce615b3aebd941732803e29d32a67d4b5","title":"The Science of the New","venue":"","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2264543182","name":"Hyeongmo Kim"},{"authorId":"2321047134","name":"Sohyun Kang"},{"authorId":"2218599338","name":"Yerin Choi"},{"authorId":"2407470561","name":"Seungyeon Ji"},{"authorId":"2066636177","name":"Junhyuk Woo"},{"authorId":"3312958","name":"Hyunsuk Chung"},{"authorId":"2408478546","name":"Soyeon Caren Han"},{"authorId":"2407767043","name":"Kyungreem Han"}],"citationStyles":{"bibtex":"@Inproceedings{Kim2026PhysicsbasedPC,\n author = {Hyeongmo Kim and Sohyun Kang and Yerin Choi and Seungyeon Ji and Junhyuk Woo and Hyunsuk Chung and Soyeon Caren Han and Kyungreem Han},\n booktitle = {arXiv.org},\n title = {Physics-based phenomenological characterization of cross-modal bias in multimodal models},\n year = {2026}\n}\n"},"paperId":"7e35c006d40863dc8aa745f9a559a87cb1edc815","title":"Physics-based phenomenological characterization of cross-modal bias in multimodal models","venue":"arXiv.org","year":2026},"contexts":["\u2026traditions for understanding human intelligence, either through the localist (Bowers, 2009; Minsky and Papert, 1969; Turing et al., 1950; Turing, 1936; Newell and Simon, 2007) or the connectionist view (Anderson and Rosenfeld, 1931; Thorndike, 1931; Minsky and Papert, 1969; Rosenblatt,\u2026"]},{"citingPaper":{"authors":[{"authorId":"2381930594","name":"J. Sanctus"}],"citationStyles":{"bibtex":"@Inproceedings{Sanctus2026PrimeLA,\n author = {J. Sanctus},\n booktitle = {Reason},\n title = {Prime Lattices and the Structure of Arithmetic: A Conceptual Note},\n year = {2026}\n}\n"},"paperId":"70ad9a69591f2798df7ef9cbd56cb1561d1f2b03","title":"Prime Lattices and the Structure of Arithmetic: A Conceptual Note","venue":"Reason","year":2026},"contexts":["54103 / 1757 - 0522 / 29911 fore captures not only numerical identity but also the limits and possibilities of computation [9, 10]."]},{"citingPaper":{"authors":[{"authorId":"2150575894","name":"Cooper Jacobus"}],"citationStyles":{"bibtex":"@Inproceedings{Jacobus2026FindingTE,\n author = {Cooper Jacobus},\n title = {Finding the Edge of Chaos in a Ferromagnet: Quantifying the\"Complexity\"of 2D Ising Phase Transitions with Image Compression},\n year = {2026}\n}\n"},"paperId":"30876b9a56dbc53150339d5390971241133610e3","title":"Finding the Edge of Chaos in a Ferromagnet: Quantifying the\"Complexity\"of 2D Ising Phase Transitions with Image Compression","venue":"","year":2026},"contexts":["1 Alan Turing\u2019s famous halting problem entails that no general algorithm can determine whether a given arbitrary program will ever finish its execution [14].","While formally uncomputable [14], the Kolmogorov complexity of any signal can be practically approximated using modern lossless compression algorithms [15]."]},{"citingPaper":{"authors":[{"authorId":"2286882243","name":"Zhimin Zhao"}],"citationStyles":{"bibtex":"@Inproceedings{Zhao2026WhyCW,\n author = {Zhimin Zhao},\n title = {Why Code, Why Now: An Information-Theoretic Perspective on the Limits of Machine Learning},\n year = {2026}\n}\n"},"paperId":"e6a907b1fc8ab303ba04d928f6a987ff2fd79971","title":"Why Code, Why Now: An Information-Theoretic Perspective on the Limits of Machine Learning","venue":"","year":2026},"contexts":["In that hierarchy, \u03a3 0 n and \u03a0 0 n sets are classified by the number of quantifier alternations in their defining formulas, and each additional alternation yields a strictly larger class of sets [41].","Turing [41] establishes the existence of problems no algorithm can solve, with the halting problem as the canonical example.","The halting language H = {\u27e8 P \u27e9 : P halts on empty input } witnesses strict containment: \u03c7 H exists as a mathematical function, but no total Turing machine computes it [41].","The halting language H is expressible ( \u03c7 H exists as a mathematical function) but not computable [41]."]},{"citingPaper":{"authors":[{"authorId":"2373035324","name":"Kamal Dingle"},{"authorId":"2267490183","name":"Marcus Hutter"}],"citationStyles":{"bibtex":"@Inproceedings{Dingle2026SimplicityAC,\n author = {Kamal Dingle and Marcus Hutter},\n booktitle = {Entropy},\n title = {Simplicity and Complexity in Combinatorial Optimization},\n year = {2026}\n}\n"},"paperId":"2dad401b5a9dd26fc17d845f240b7c5509e20709","title":"Simplicity and Complexity in Combinatorial Optimization","venue":"Entropy","year":2026},"contexts":["More formally, the Kolmogorov complexity K U ( x ) of a string x with respect to a (prefix optimal) universal Turing machine [17] (UTM) U , is defined [12\u201314] as K V ( x ) | \u2264 c so that the complexity of x is independent of the choice of the machine, to within an additive constant c ."]},{"citingPaper":{"authors":[{"authorId":"2342783426","name":"Marvin Tritschler"}],"citationStyles":{"bibtex":"@Inproceedings{Tritschler2026TheTT,\n author = {Marvin Tritschler},\n booktitle = {Theoria},\n title = {The Turing Test as a Sceptical Scenario},\n year = {2026}\n}\n"},"paperId":"037c86b4173c22e7f91f333d0ad19ad9efa7540f","title":"The Turing Test as a Sceptical Scenario","venue":"Theoria","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2413141117","name":"Filipe Dinis Bernardino"},{"authorId":"104853879","name":"Marisa Dinis"}],"citationStyles":{"bibtex":"@Inproceedings{Bernardino2026AIA,\n author = {Filipe Dinis Bernardino and Marisa Dinis},\n booktitle = {Brazilian Journal of Business},\n title = {A intelig\u00eancia artificial na decis\u00e3o empresarial razo\u00e1vel - uma breve perspetiva do direito portugu\u00eas},\n year = {2026}\n}\n"},"paperId":"308355e76790d8771d690a19a1266dae3096285c","title":"A intelig\u00eancia artificial na decis\u00e3o empresarial razo\u00e1vel - uma breve perspetiva do direito portugu\u00eas","venue":"Brazilian Journal of Business","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2397954153","name":"Fernando Rodriguez-Vergara"},{"authorId":"2372071225","name":"Phil Husbands"}],"citationStyles":{"bibtex":"@Inproceedings{Rodriguez-Vergara2026IsEC,\n author = {Fernando Rodriguez-Vergara and Phil Husbands},\n booktitle = {Mathematics},\n title = {Is Every Cognitive Phenomenon Computable?},\n year = {2026}\n}\n"},"paperId":"03d2de220e1ebd806773fc9477bad2495a211569","title":"Is Every Cognitive Phenomenon Computable?","venue":"Mathematics","year":2026},"contexts":["Considering that computers at that time were humans, the idea of an algorithm as formalized by Turing [17], namely as a well-defined machine that could essentially perform the same job as a human computer with pen and paper, was most appealing.","In fact, this is why in [17], irrational numbers such as \u03c0 and e are considered computable: Because a number of decimal digits has to be specified for the function, and even if that number is incredibly large, given that the coefficients of the series follow a computable sequence, they can be\u2026","\u2026known to us has the same computational power [23\u201325 The development of these ideas went as follows: A formal definition for the notion of algorithm was introduced by Church [20] and Turing [17] through lambda calculus and Turing machines, respectively [26], entailing that they are equivalent.","If we go all the way back to Turing\u2019s [17] seminal paper on computable numbers, then a central difference is explicitly made between automatic or a machines, and choice or c machines (those that will require an external operator to eventually make choices for them).","This intuitive notion was replaced by a formal one, provided by the works of Church [20,21] and Turing [17].","The underlying premise is that these problems can be resolved mechanically (in the sense of automatically); that is, they can be solved without requiring mathematical knowledge about the logical steps involved [17,18]."]},{"citingPaper":{"authors":[{"authorId":"2003547314","name":"Yannik N. B\u00f6ck"},{"authorId":"2256994240","name":"Holger Boche"},{"authorId":"2283708820","name":"Z. G. del Toro"},{"authorId":"2319306576","name":"F. Fitzek"}],"citationStyles":{"bibtex":"@Inproceedings{B\u00f6ck2026FeynmanMT,\n author = {Yannik N. B\u00f6ck and Holger Boche and Z. G. del Toro and F. Fitzek},\n booktitle = {IEEE transactions on computers},\n title = {Feynman Meets Turing: Computability Aspects of Quantum Compiling Revisited},\n year = {2026}\n}\n"},"paperId":"b683e6e21a62d1abab2c179106b12212cc5487cc","title":"Feynman Meets Turing: Computability Aspects of Quantum Compiling Revisited","venue":"IEEE transactions on computers","year":2026},"contexts":["As indicated in Section II, effective analysis builds upon the work of Alan M. Turing [26], [27]."]},{"citingPaper":{"authors":[{"authorId":"2408288534","name":"Youngwoong Cho"}],"citationStyles":{"bibtex":"@Inproceedings{Cho2026WhatIT,\n author = {Youngwoong Cho},\n booktitle = {arXiv.org},\n title = {What is the AGI in Offensive Security ?},\n year = {2026}\n}\n"},"paperId":"b513e88b7e5638f01f823c68ceab4c3af034cd68","title":"What is the AGI in Offensive Security ?","venue":"arXiv.org","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2363724234","name":"Vikash Singh"},{"authorId":"41020843","name":"Darion Cassel"},{"authorId":"38912638","name":"Nathaniel Weir"},{"authorId":"2280064937","name":"Nick Feng"},{"authorId":"2390933656","name":"Sam Bayless"}],"citationStyles":{"bibtex":"@Inproceedings{Singh2026VERGEFR,\n author = {Vikash Singh and Darion Cassel and Nathaniel Weir and Nick Feng and Sam Bayless},\n booktitle = {arXiv.org},\n title = {VERGE: Formal Refinement and Guidance Engine for Verifiable LLM Reasoning},\n year = {2026}\n}\n"},"paperId":"1e0bf224a6129946f76e6ed6880fc207f807bdf3","title":"VERGE: Formal Refinement and Guidance Engine for Verifiable LLM Reasoning","venue":"arXiv.org","year":2026},"contexts":["Prior neuro-symbolic integration (Mao et al., 2019; Garcez et al., 2019; Kautz, 2022) and grammar-based approaches (Ganguly et al., 2024) struggle with the semantic gap (Church, 1936; Turing, 1936) the mismatch between ambiguous natural language and rigid formal systems.","However, these approaches face a fundamental semantic gap : natural language is inherently ambiguous, and rigid formalization often fails on open-domain claims (Church, 1936; Turing, 1936)."]},{"citingPaper":{"authors":[{"authorId":"2404601038","name":"Baruch Garcia"}],"citationStyles":{"bibtex":"@Inproceedings{Garcia2026DiagonalizationWR,\n author = {Baruch Garcia},\n booktitle = {arXiv.org},\n title = {Diagonalization Without Relativization A Closer Look at the Baker-Gill-Solovay Theorem},\n year = {2026}\n}\n"},"paperId":"c7ef4848c31d324f0beb64f08d784f79bffc55e1","title":"Diagonalization Without Relativization A Closer Look at the Baker-Gill-Solovay Theorem","venue":"arXiv.org","year":2026},"contexts":["Historically, the undecidability of the halting problem discovered by Turing[37]\u2014on the heels of G\u00a8odel\u2019s demonstration of the existence of undecidable propositions in Peano arithmetic[16]\u2014reigns supreme as the foundation and gold standard for computability theory."]},{"citingPaper":{"authors":[{"authorId":"2350582428","name":"Liang Wen"}],"citationStyles":{"bibtex":"@Inproceedings{Wen2026LimitedMA,\n author = {Liang Wen},\n booktitle = {Foundations of Science},\n title = {Limited Math: Aligning Mathematical Semantics with Finite Computation},\n year = {2026}\n}\n"},"paperId":"f6256a6b0f3241d2ae81164700ccb85db668dfdb","title":"Limited Math: Aligning Mathematical Semantics with Finite Computation","venue":"Foundations of Science","year":2026},"contexts":["Even fundamental questions such as termination are undecidable in classical models of computation [15, 14], despite the fact that bounded machines induce finite state spaces.","These abstractions underpin foundational results such as the undecidability of the halting problem [15] and remain indispensable to theoretical computer science [14]."]},{"citingPaper":{"authors":[{"authorId":"2320311999","name":"Takuya Isomura"}],"citationStyles":{"bibtex":"@Inproceedings{Isomura2026TripleEI,\n author = {Takuya Isomura},\n booktitle = {Neurosciences research},\n title = {Triple equivalence in modelling insight and creativity: classical and quantum perspectives.},\n year = {2026}\n}\n"},"paperId":"bbd8e5d93b6aef5d2e42d128ed397d905c881f5a","title":"Triple equivalence in modelling insight and creativity: classical and quantum perspectives.","venue":"Neurosciences research","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2237834784","name":"Eliahu Cohen"}],"citationStyles":{"bibtex":"@Inproceedings{Cohen2026AgencyUP,\n author = {Eliahu Cohen},\n booktitle = {NATURAL SCIENCES},\n title = {Agency Under Prediction: A Review of The Human Test},\n year = {2026}\n}\n"},"paperId":"cd62c473fa3b3a80020cbd07948ddd59d2b98933","title":"Agency Under Prediction: A Review of The Human Test","venue":"NATURAL SCIENCES","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2059238705","name":"R. Magee"},{"authorId":"4282473","name":"M. Mupparapu"}],"citationStyles":{"bibtex":"@Inproceedings{Magee2026IntroductionTM,\n author = {R. Magee and M. Mupparapu},\n booktitle = {Dental Clinics of North America},\n title = {Introduction to Methods in Artificial Intelligence and Cognitive Neurology.},\n year = {2026}\n}\n"},"paperId":"d834812f96f7a7c677cc631e470040ed21a3cc69","title":"Introduction to Methods in Artificial Intelligence and Cognitive Neurology.","venue":"Dental Clinics of North America","year":2026},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2269147580","name":"Alex Lewandowski"},{"authorId":"2401492460","name":"A. Ramesh"},{"authorId":"2269466069","name":"Edan Meyer"},{"authorId":"2269148177","name":"Dale Schuurmans"},{"authorId":"2394592482","name":"Marlos C. Machado"}],"citationStyles":{"bibtex":"@Inproceedings{Lewandowski2025TheWI,\n author = {Alex Lewandowski and A. Ramesh and Edan Meyer and Dale Schuurmans and Marlos C. Machado},\n booktitle = {arXiv.org},\n title = {The World Is Bigger! A Computationally-Embedded Perspective on the Big World Hypothesis},\n year = {2025}\n}\n"},"paperId":"fb8b89229e84788a1f3a368709541d06edef021a","title":"The World Is Bigger! A Computationally-Embedded Perspective on the Big World Hypothesis","venue":"arXiv.org","year":2025},"contexts":["Our approach is general, by making use of the Church-Turing thesis, which asserts that all computationally universal systems are equivalent in what they can simulate, and that any such system can simulate another (Church, 1936; Turing, 1937).","Computational universality guarantees that the environment can simulate any algorithm (Church, 1936; Turing, 1937)."]},{"citingPaper":{"authors":[{"authorId":"2049085100","name":"Madalina I. Sas"},{"authorId":"46387264","name":"Julian Sutherland"}],"citationStyles":{"bibtex":"@Inproceedings{Sas2025RandomSC,\n author = {Madalina I. Sas and Julian Sutherland},\n booktitle = {arXiv.org},\n title = {Random state comonads encode cellular automata evaluation},\n year = {2025}\n}\n"},"paperId":"b6b5441ef9efa83480ba34b8f4c75e427477b18f","title":"Random state comonads encode cellular automata evaluation","venue":"arXiv.org","year":2025},"contexts":["Turing machines treat computation as a sequence of transitions between states expressed as symbol manipulations on a tape, emphasising how to compute (Turing 1936) \u2013 naturally expressing step-by-step procedural programming."]},{"citingPaper":{"authors":[{"authorId":"2263721434","name":"Eva Miranda"},{"authorId":"2400149592","name":"I. Ramos"}],"citationStyles":{"bibtex":"@Inproceedings{Miranda2025ClassicalBC,\n author = {Eva Miranda and I. Ramos},\n booktitle = {arXiv.org},\n title = {Classical billiards can compute},\n year = {2025}\n}\n"},"paperId":"82d78df4c66ddb49196c236446f3f8a44340cc05","title":"Classical billiards can compute","venue":"arXiv.org","year":2025},"contexts":["An interesting outcome of this construction is that the undecidability of the Halting problem [30] implies the undecidability of classical billiard systems.","As a result, basic dynamical questions, including the existence of periodic trajectories become algorithmically undecidable [30, 24].","Isaac Ramos is supported by a fellowship from \u201cLa Caixa\u201d Foundation (ID 100010434) with code LCF/BQ/PFA25/11000070. phenomena rooted in Turing\u2019s Halting problem [30]."]},{"citingPaper":{"authors":[{"authorId":"2349238241","name":"Abhisek Ganguly"}],"citationStyles":{"bibtex":"@Inproceedings{Ganguly2025DualCH,\n author = {Abhisek Ganguly},\n booktitle = {arXiv.org},\n title = {Dual Computational Horizons: Incompleteness and Unpredictability in Intelligent Systems},\n year = {2025}\n}\n"},"paperId":"714de229f28a91345af4a2278145efbf7e1a9ec2","title":"Dual Computational Horizons: Incompleteness and Unpredictability in Intelligent Systems","venue":"arXiv.org","year":2025},"contexts":["G\u00f6del incompleteness puts constraints on the formal reasoning in AI [1, 2, 5], while chaos theory establishes limits on long-term prediction [3, 4].","Formally, the set { t | R \u22a2 ( P t \u2248 F t ) } is not computable, as its complement relates to the halting problem: R cannot decide if divergent simulations \u201chalt within \u03b4 \u201d [2].","Formal incompleteness: No consistent system capable of arithmetic can be deductively complete [1, 2]."]},{"citingPaper":{"authors":[{"authorId":"2327547690","name":"Borjan Milinkovic"},{"authorId":"2265731392","name":"Jaan Aru"}],"citationStyles":{"bibtex":"@Inproceedings{Milinkovic2025OnBA,\n author = {Borjan Milinkovic and Jaan Aru},\n booktitle = {Neuroscience and Biobehavioral Reviews},\n title = {On biological and artificial consciousness: A case for biological computationalism.},\n year = {2025}\n}\n"},"paperId":"7087ab154aefc974b477596488e852d645b0de9a","title":"On biological and artificial consciousness: A case for biological computationalism.","venue":"Neuroscience and Biobehavioral Reviews","year":2025},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2257767092","name":"Hanyu Li"},{"authorId":"84292561","name":"Xiaotie Deng"}],"citationStyles":{"bibtex":"@Inproceedings{Li2025WillAT,\n author = {Hanyu Li and Xiaotie Deng},\n booktitle = {arXiv.org},\n title = {Will AI Trade? A Computational Inversion of the No-Trade Theorem},\n year = {2025}\n}\n"},"paperId":"6f55001f76de92349f8f894b283259b5bcb47e2e","title":"Will AI Trade? A Computational Inversion of the No-Trade Theorem","venue":"arXiv.org","year":2025},"contexts":["A Turing Machine (TM) [25] is a foundational model of computation."]},{"citingPaper":{"authors":[{"authorId":"2350753497","name":"Erik Hoel"}],"citationStyles":{"bibtex":"@Inproceedings{Hoel2025ADO,\n author = {Erik Hoel},\n booktitle = {arXiv.org},\n title = {A Disproof of Large Language Model Consciousness: The Necessity of Continual Learning for Consciousness},\n year = {2025}\n}\n"},"paperId":"9cf0f99db8c791a44baf731cd36d67c0fe28d802","title":"A Disproof of Large Language Model Consciousness: The Necessity of Continual Learning for Consciousness","venue":"arXiv.org","year":2025},"contexts":["Here and throughout, such strictly-dependent-on-inferences theories of consciousness are referred to as \u201ctrivial\u201d to clearly distinguish that the source of the unfalsifiability is coming from strict dependency holding true."]},{"citingPaper":{"authors":[{"authorId":"2368754593","name":"R. Ilango"}],"citationStyles":{"bibtex":"@Inproceedings{Ilango2025G\u00f6delIC,\n author = {R. Ilango},\n booktitle = {IEEE Annual Symposium on Foundations of Computer Science},\n title = {G\u00f6del in Cryptography: Effectively Zero-Knowledge Proofs for NP with No Interaction, No Setup, and Perfect Soundness},\n year = {2025}\n}\n"},"paperId":"0df4c0e22f2051f7a4d2f4e898d40dc52ef287c7","title":"G\u00f6del in Cryptography: Effectively Zero-Knowledge Proofs for NP with No Interaction, No Setup, and Perfect Soundness","venue":"IEEE Annual Symposium on Foundations of Computer Science","year":2025},"contexts":["Theorem III.9 ([45, 67]) ."]},{"citingPaper":{"authors":[{"authorId":"2380442692","name":"Milan Rosko"}],"citationStyles":{"bibtex":"@Inproceedings{Rosko2025AdversarialBI,\n author = {Milan Rosko},\n booktitle = {arXiv.org},\n title = {Adversarial Barrier in Uniform Class Separation},\n year = {2025}\n}\n"},"paperId":"f69ad4e9fb2f12f746cc2379968467a2e78b6149","title":"Adversarial Barrier in Uniform Class Separation","venue":"arXiv.org","year":2025},"contexts":["These constrained permutations admit a reverse Halting [Turing, 1937, 1938] predicate: the solver must \u201cspeak\u201d the problem language in order to enumerate it."]},{"citingPaper":{"authors":[{"authorId":"2957805","name":"Simon M. Huttegger"},{"authorId":"2294175451","name":"Sean Walsh"},{"authorId":"2281473814","name":"Francesca Zaffora Blando"}],"citationStyles":{"bibtex":"@Inproceedings{Huttegger2025BayesianCF,\n author = {Simon M. Huttegger and Sean Walsh and Francesca Zaffora Blando},\n booktitle = {Philosophy and Phenomenological Research},\n title = {Bayesian Convergence for Computably Bounded Agents},\n year = {2025}\n}\n"},"paperId":"de4313481cf3c32454ab150c5a3faca4922c86cb","title":"Bayesian Convergence for Computably Bounded Agents","venue":"Philosophy and Phenomenological Research","year":2025},"contexts":["These low levels of the Borel hierarchy are the propositions that one can form from the open sets by using a finite number of the operations of negation and natural number quantification."]},{"citingPaper":{"authors":[{"authorId":"2363493870","name":"Georgios Mappouras"},{"authorId":"3397968","name":"C. Rossides"}],"citationStyles":{"bibtex":"@Inproceedings{Mappouras2025OnTC,\n author = {Georgios Mappouras and C. Rossides},\n booktitle = {arXiv.org},\n title = {On the Computability of Artificial General Intelligence},\n year = {2025}\n}\n"},"paperId":"1116efe5a58a0f5114c2942450755072f0b50288","title":"On the Computability of Artificial General Intelligence","venue":"arXiv.org","year":2025},"contexts":["A. Church [37] and A. Turing [38] pose and discuss the fundamental question of computability, i.e. which mathematical problems can be solved by a step-by-step (mechanical) process.","One famous such example is the Halting Problem were asking if an algorithm (or Turing Machine) ever halts is an undecidable problem as proved by Alan Turing [38]."]},{"citingPaper":{"authors":[{"authorId":"2328643882","name":"A. Alyakin"}],"citationStyles":{"bibtex":"@Inproceedings{Alyakin2025AllYN,\n author = {A. Alyakin},\n booktitle = {arXiv.org},\n title = {\"All You Need\" is Not All You Need for a Paper Title: On the Origins of a Scientific Meme},\n year = {2025}\n}\n"},"paperId":"a389e5619fe4c531cfd333645dc070d48c9c4699","title":"\"All You Need\" is Not All You Need for a Paper Title: On the Origins of a Scientific Meme","venue":"arXiv.org","year":2025},"contexts":["Mathematics and physics have long favored the \u201cOn X\u201d construction\u2014exemplified by Turing\u2019s foundational \u201cOn Computable Numbers\u201d [26] and Einstein\u2019s \u201cOn the Electrodynamics of Moving Bodies\u201d [27]\u2014a convention dating to classical trea-tises, perhaps signaling scholarly modesty."]},{"citingPaper":{"authors":[{"authorId":"2290013181","name":"Stephen Fitz"}],"citationStyles":{"bibtex":"@Inproceedings{Fitz2025TestingTM,\n author = {Stephen Fitz},\n booktitle = {arXiv.org},\n title = {Testing the Machine Consciousness Hypothesis},\n year = {2025}\n}\n"},"paperId":"bd97f73e21cca990f4cd35d0fe96206fac41fcd7","title":"Testing the Machine Consciousness Hypothesis","venue":"arXiv.org","year":2025},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"41049716","name":"Paula Quinon"}],"citationStyles":{"bibtex":"@Inproceedings{Quinon2025IntensionalDB,\n author = {Paula Quinon},\n booktitle = {Philosophies},\n title = {Intensional Differences Between Programming Languages: A Conceptual and Practical Analysis},\n year = {2025}\n}\n"},"paperId":"26d07e62e110177da15eb77abed45df15e667bfe","title":"Intensional Differences Between Programming Languages: A Conceptual and Practical Analysis","venue":"Philosophies","year":2025},"contexts":["\u2026which emphasize state transitions and mechanical procedures and are more directly associated with the idea of algorithmic step-by-step execution [10], and recursive functions, which reflect a model grounded in arithmetic and bounded computation [11,12], are best understood as different\u2026"]},{"citingPaper":{"authors":[{"authorId":"153604150","name":"Andres Campero"},{"authorId":"2393205697","name":"Derek Shiller"},{"authorId":"2075928","name":"Jaan Aru"},{"authorId":"2265347520","name":"Jonathan Simon"}],"citationStyles":{"bibtex":"@Inproceedings{Campero2025ConsciousnessIA,\n author = {Andres Campero and Derek Shiller and Jaan Aru and Jonathan Simon},\n booktitle = {arXiv.org},\n title = {Consciousness in Artificial Intelligence? A Framework for Classifying Objections and Constraints},\n year = {2025}\n}\n"},"paperId":"e93825127979f349b3451b0222f4866df8c812c2","title":"Consciousness in Artificial Intelligence? A Framework for Classifying Objections and Constraints","venue":"arXiv.org","year":2025},"contexts":["Turing, in an appendix to his 1936 paper [14], proved the extensional equivalence of his and Church\u2019s two formal characterizations."]},{"citingPaper":{"authors":[{"authorId":"51153095","name":"Linzhuo Li"},{"authorId":"2289032471","name":"Yilin Lin"},{"authorId":"2246929716","name":"Lingfei Wu"}],"citationStyles":{"bibtex":"@Inproceedings{Li2025InnovationBD,\n author = {Linzhuo Li and Yilin Lin and Lingfei Wu},\n booktitle = {arXiv.org},\n title = {Innovation by Displacement},\n year = {2025}\n}\n"},"paperId":"78982ef2dcd76757fc020e87132c3ad03433c0f9","title":"Innovation by Displacement","venue":"arXiv.org","year":2025},"contexts":["Turing\u2019s (1936) paper exemplifies this dynamic.","Turing\u2019s (1936) paper\u2014rooted entirely in mainstream mathematics and logic\u2014illustrates this point."]},{"citingPaper":{"authors":[{"authorId":"2398798960","name":"Evan Redden"}],"citationStyles":{"bibtex":"@Inproceedings{Redden2025ProvabilityVE,\n author = {Evan Redden},\n title = {Provability vs. Execution: A Comment on\"Consequences of Undecidability in Physics on the Theory of Everything\"},\n year = {2025}\n}\n"},"paperId":"09e19e3846aa03fe5836ae9b99e2556cc943f95f","title":"Provability vs. Execution: A Comment on\"Consequences of Undecidability in Physics on the Theory of Everything\"","venue":"","year":2025},"contexts":["To argue that our universe cannot be simulated algorithmically, one must demonstrate that physical processes require computational resources beyond those available to a Turing machine [8]."]},{"citingPaper":{"authors":[{"authorId":"2402064121","name":"Miroslav Lzicar"}],"citationStyles":{"bibtex":"@Inproceedings{Lzicar2025CellARCMI,\n author = {Miroslav Lzicar},\n booktitle = {arXiv.org},\n title = {CellARC: Measuring Intelligence with Cellular Automata},\n year = {2025}\n}\n"},"paperId":"ba57e011a0f68c7002c327743a3d1abb8dbf672f","title":"CellARC: Measuring Intelligence with Cellular Automata","venue":"arXiv.org","year":2025},"contexts":["\u2026large class of rational functions and practical string-to-string mappings (Choffrut, 2003; Mohri, 1997); and Turing-complete substrates (e.g., small universal machines, or universal CA such as Rule 110) to stress algo-rithm learning and memory use (Turing, 1936; Cook, 2004; Hopcroft et al., 2006)."]},{"citingPaper":{"authors":[{"authorId":"2355648946","name":"Anjani kumar Polinati"}],"citationStyles":{"bibtex":"@Inproceedings{Polinati2025HybridQD,\n author = {Anjani kumar Polinati},\n booktitle = {2025 Tenth International Conference on Science Technology Engineering and Mathematics (ICONSTEM)},\n title = {Hybrid Quantum-Classical Deep Reinforcement Learning for Autonomous Deception-Based Cyber Defense in Cloud Infrastructures},\n year = {2025}\n}\n"},"paperId":"4fbe37e0fa370a3ffbf09f1da8dffde0e65160e1","title":"Hybrid Quantum-Classical Deep Reinforcement Learning for Autonomous Deception-Based Cyber Defense in Cloud Infrastructures","venue":"2025 Tenth International Conference on Science Technology Engineering and Mathematics (ICONSTEM)","year":2025},"contexts":["The current work extends previous work in the ML; DL and quantum fields and proposes a new method to protect the cloud infrastructures against the new security risks [8]."]},{"citingPaper":{"authors":[{"authorId":"2390494630","name":"David Kattermann"},{"authorId":"102665792","name":"L. S. Krapp"}],"citationStyles":{"bibtex":"@Inproceedings{Kattermann2025RecursivelyER,\n author = {David Kattermann and L. S. Krapp},\n booktitle = {arXiv.org},\n title = {Recursively Enumerably Representable Classes and Computable Versions of the Fundamental Theorem of Statistical Learning},\n year = {2025}\n}\n"},"paperId":"b5f7242e377444462e4219e2a1cdfab66566ce97","title":"Recursively Enumerably Representable Classes and Computable Versions of the Fundamental Theorem of Statistical Learning","venue":"arXiv.org","year":2025},"contexts":["We do not assume any background in computability theory here beyond the basic notion of computability, for instance via Turing machines [T36]."]},{"citingPaper":{"authors":[{"authorId":"2344170175","name":"Angelos Gkekas"},{"authorId":"1712127775","name":"Nikos A. Mitsiou"},{"authorId":"2390396365","name":"Ioannis Souldatos"},{"authorId":"144015029","name":"G. Karagiannidis"}],"citationStyles":{"bibtex":"@Inproceedings{Gkekas2025OnTC,\n author = {Angelos Gkekas and Nikos A. Mitsiou and Ioannis Souldatos and G. Karagiannidis},\n booktitle = {arXiv.org},\n title = {On the Computability of Finding Capacity-Achieving Codes},\n year = {2025}\n}\n"},"paperId":"5fdc1681e21eaf0c31809e899878404cc818e43b","title":"On the Computability of Finding Capacity-Achieving Codes","venue":"arXiv.org","year":2025},"contexts":["Turing machines, introduced by Turing in his seminal work [6], constitute the earliest and most widely used formal model of computation, and are regarded as the foundation of theoretical computer science.","These concepts can be traced back to the works of G\u00a8odel [7], Turing [6], and Kleene [8], [16], [17].","The most widely used formal model of computation is the Turing machine , introduced by Alan Turing in his seminal work on the Entscheidungsproblem [6].","The class of computable real numbers was first defined by Turing in the same work in which he introduced Turing machines [6]."]},{"citingPaper":{"authors":[{"authorId":"2144257643","name":"Yong Chen"}],"citationStyles":{"bibtex":"@Inproceedings{Chen2025SynstorCF,\n author = {Yong Chen},\n title = {Synstor circuits for real-time adaptive intelligent systems},\n year = {2025}\n}\n"},"paperId":"f60739cbb22372f66bf06168fab7dc669bfb133c","title":"Synstor circuits for real-time adaptive intelligent systems","venue":"","year":2025},"contexts":["The prevailing method for building artificial intelligence (AI) systems centers on digital computers based on the Turing model (Turing, 1936)."]},{"citingPaper":{"authors":[{"authorId":"2330078738","name":"Shairoz Sohail"},{"authorId":"2390202439","name":"T. Ali"}],"citationStyles":{"bibtex":"@Inproceedings{Sohail2025TowardsAM,\n author = {Shairoz Sohail and T. Ali},\n booktitle = {arXiv.org},\n title = {Towards a Measure of Algorithm Similarity},\n year = {2025}\n}\n"},"paperId":"e6f44ee6b1bf1ff484a9f1ace67b534269125d1e","title":"Towards a Measure of Algorithm Similarity","venue":"arXiv.org","year":2025},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2397383250","name":"D. Abdullah"},{"authorId":"2397379200","name":"Jasem Hamoud"}],"citationStyles":{"bibtex":"@Inproceedings{Abdullah2025ASO,\n author = {D. Abdullah and Jasem Hamoud},\n booktitle = {arXiv.org},\n title = {A Study of NP-Completeness and Undecidable Word Problems in Semigroups},\n year = {2025}\n}\n"},"paperId":"5134119a10e1737791cf764ce6b5d759e3eb14da","title":"A Study of NP-Completeness and Undecidable Word Problems in Semigroups","venue":"arXiv.org","year":2025},"contexts":["This result connects to the broader landscape of undecidability established by Turing [10] and Church [11], reinforcing the understanding that certain mathematical problems lie beyond the reach of computational methods, regardless of available resources or time.","The study of undecidable problems traces back to the groundbreaking work of Turing [10] and Church [11], who independently demonstrated the existence of problems that cannot be solved by any algorithm."]},{"citingPaper":{"authors":[{"authorId":"2025369676","name":"Adam Winchell"}],"citationStyles":{"bibtex":"@Inproceedings{Winchell2025CanMT,\n author = {Adam Winchell},\n booktitle = {arXiv.org},\n title = {Can machines think efficiently?},\n year = {2025}\n}\n"},"paperId":"638a168af50cb28aaaeed96da0fa0a656097a3e7","title":"Can machines think efficiently?","venue":"arXiv.org","year":2025},"contexts":["20"]},{"citingPaper":{"authors":[{"authorId":"2192607174","name":"Juan Esteban Suarez Cardona"},{"authorId":"2280062784","name":"Holger Boche"},{"authorId":"3125779","name":"Gitta Kutyniok"}],"citationStyles":{"bibtex":"@Inproceedings{Cardona2025AVF,\n author = {Juan Esteban Suarez Cardona and Holger Boche and Gitta Kutyniok},\n booktitle = {arXiv.org},\n title = {A Variational Framework for the Algorithmic Complexity of PDE Solutions},\n year = {2025}\n}\n"},"paperId":"7e446040d752833c510d6edad56ba65e47932948","title":"A Variational Framework for the Algorithmic Complexity of PDE Solutions","venue":"arXiv.org","year":2025},"contexts":["Yet, the fundamental question of Turing computability [1] of PDE solutions has only been addressed to a limited extent."]},{"citingPaper":{"authors":[{"authorId":"2387862028","name":"Bentley DeVilling"}],"citationStyles":{"bibtex":"@Inproceedings{DeVilling2025TheML,\n author = {Bentley DeVilling},\n booktitle = {arXiv.org},\n title = {The Mirror Loop: Recursive Non-Convergence in Generative Reasoning Systems},\n year = {2025}\n}\n"},"paperId":"babe72fb873ba7e56b7c78de4c77f9193a37b68f","title":"The Mirror Loop: Recursive Non-Convergence in Generative Reasoning Systems","venue":"arXiv.org","year":2025},"contexts":["Turing\u2019s halting problem proves that no general procedure can determine whether arbitrary self-referential computation will terminate [6]."]},{"citingPaper":{"authors":[{"authorId":"1688430","name":"M. Ghayoumi"},{"authorId":"2883129","name":"Kambiz Ghazinour"}],"citationStyles":{"bibtex":"@Inproceedings{Ghayoumi2025HumanRI,\n author = {M. Ghayoumi and Kambiz Ghazinour},\n booktitle = {Ubiquitous Computing, Electronics & Mobile Communication Conference},\n title = {Human Rights in the Shadow of AI: Confronting Bias and Accountability},\n year = {2025}\n}\n"},"paperId":"35d7cc55eeb72f9cf2c6d87f311978d1ef539856","title":"Human Rights in the Shadow of AI: Confronting Bias and Accountability","venue":"Ubiquitous Computing, Electronics & Mobile Communication Conference","year":2025},"contexts":["In both contexts, accountability becomes a shell game, passed between developers, deploying organizations, and end-users until it disappears altogether [15][19][27][38]."]},{"citingPaper":{"authors":[{"authorId":"2390654171","name":"Giovanni Pilato"},{"authorId":"48954492","name":"Filippo Vella"},{"authorId":"2404500993","name":"Tommaso Brugarino"},{"authorId":"34277167","name":"S. Gaglio"}],"citationStyles":{"bibtex":"@Inproceedings{Pilato2025TowardsQL,\n author = {Giovanni Pilato and Filippo Vella and Tommaso Brugarino and S. Gaglio},\n booktitle = {2025 IEEE Conference on Pervasive and Intelligent Computing (PICom)},\n title = {Towards Quantum Logic Programming},\n year = {2025}\n}\n"},"paperId":"999018f5a352046d4090e6bc270fe75a0b631f49","title":"Towards Quantum Logic Programming","venue":"2025 IEEE Conference on Pervasive and Intelligent Computing (PICom)","year":2025},"contexts":["Furthermore, they are equivalent to the Universal Turing Machine(UTM) [10]."]},{"citingPaper":{"authors":[{"authorId":"2281193844","name":"Eilene Tomkins-Flanagan"},{"authorId":"2386617504","name":"Connor Hanley"},{"authorId":"2281092268","name":"M. A. Kelly"}],"citationStyles":{"bibtex":"@Inproceedings{Tomkins-Flanagan2025HeyPW,\n author = {Eilene Tomkins-Flanagan and Connor Hanley and M. A. Kelly},\n booktitle = {arXiv.org},\n title = {Hey Pentti, We Did It Again!: Differentiable vector-symbolic types that prove polynomial termination},\n year = {2025}\n}\n"},"paperId":"923ac2e028b909f70ab58ba1ff2c3386f0208814","title":"Hey Pentti, We Did It Again!: Differentiable vector-symbolic types that prove polynomial termination","venue":"arXiv.org","year":2025},"contexts":["\u2026because it involves comparing programs in light of their computational effects, and some programs cannot be proven either to eventually halt or run forever (Turing, 1936), so their computational effects cannot be known either until they halt or until the end of time, whichever comes first."]},{"citingPaper":{"authors":[{"authorId":"2055117902","name":"Siyuan Qiu"},{"authorId":"2373170768","name":"Jianfeng Xu"}],"citationStyles":{"bibtex":"@Inproceedings{Qiu2025ResearchOA,\n author = {Siyuan Qiu and Jianfeng Xu},\n booktitle = {Mathematics},\n title = {Research on a General State Formalization Method from the Perspective of Logic},\n year = {2025}\n}\n"},"paperId":"0a769ddd7e4236500ad3e7da8218a079eef76e30","title":"Research on a General State Formalization Method from the Perspective of Logic","venue":"Mathematics","year":2025},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"3034012","name":"V. Stankovski"}],"citationStyles":{"bibtex":"@Inproceedings{Stankovski2025FromOB,\n author = {V. Stankovski},\n booktitle = {International Conference on Blockchain Computing and Applications},\n title = {From One Bit to Meaningful Self: Recursive Identity Formation for Decentralized Digital Trust},\n year = {2025}\n}\n"},"paperId":"2cc6cafe4dc884f3b0f95899e03bf3f608a3ec80","title":"From One Bit to Meaningful Self: Recursive Identity Formation for Decentralized Digital Trust","venue":"International Conference on Blockchain Computing and Applications","year":2025},"contexts":["System B corresponds to the classical , binary logic-based decision-making paradigm grounded in Turing-computability [1], [2]."]},{"citingPaper":{"authors":[{"authorId":"2385784856","name":"Hieu Le Duc"},{"authorId":"2263205667","name":"Leo Liberti"}],"citationStyles":{"bibtex":"@Inproceedings{Duc2025MathematicsWL,\n author = {Hieu Le Duc and Leo Liberti},\n booktitle = {arXiv.org},\n title = {Mathematics with large language models as provers and verifiers},\n year = {2025}\n}\n"},"paperId":"818a975687080228e9994d5dfcc42ed6dec73caf","title":"Mathematics with large language models as provers and verifiers","venue":"arXiv.org","year":2025},"contexts":["Alan Turing conceived his computational model of the computer not only as a mechanical way of performing computations [27], and not only as a precise definition of the Leibnitzian calculemus dream, with roots in Renaissance steganographers, whose influence crept through the centuries to reach\u2026","Since this graph is infinite, the search for the path leading from the axioms to the conclusion of the desired theorem statement may be indefinitely long, and establishing unprovability yields a non-terminating search (this is exactly the \u201cEntscheidungsproblem\u201d that Turing settled in [27])."]},{"citingPaper":{"authors":[{"authorId":"2383169506","name":"Milan Rosko"}],"citationStyles":{"bibtex":"@Inproceedings{Rosko2025TheFL,\n author = {Milan Rosko},\n booktitle = {arXiv.org},\n title = {The Fractal Logic of \u03a6-adic Recursion},\n year = {2025}\n}\n"},"paperId":"89130c5b6095e04c5be76ce001a8ab85f21878d9","title":"The Fractal Logic of \u03a6-adic Recursion","venue":"arXiv.org","year":2025},"contexts":["\u2014treated by Church [1936] and Turing [1937, 1938]\u2014Formally: let P denote the set of all decidable subproblems.","A parallel geometric interpretation of incompleteness emerges, distinct from the Church-Turing thesis\u2019s computational interpretation, that is not dependent on the existence of [Turing, 1937] machines ( M ) but geometry."]},{"citingPaper":{"authors":[{"authorId":"2384766086","name":"Liang Mao"},{"authorId":"2374322856","name":"Laura Cui"},{"authorId":"2310609932","name":"T. Schuster"},{"authorId":"2319873302","name":"Hsin-Yuan Huang"}],"citationStyles":{"bibtex":"@Inproceedings{Mao2025RandomUT,\n author = {Liang Mao and Laura Cui and T. Schuster and Hsin-Yuan Huang},\n booktitle = {arXiv.org},\n title = {Random unitaries that conserve energy},\n year = {2025}\n}\n"},"paperId":"d0b6d176bed914fdce30954138324ad738a0e112","title":"Random unitaries that conserve energy","venue":"arXiv.org","year":2025},"contexts":["Since we are taking TMs as inputs, the existence of energy-conserving PRUs can be linked to the solution of the halting problem, a canonical undecidable problem [69, 70]."]},{"citingPaper":{"authors":[{"authorId":"2070680937","name":"Kartik Chandra"},{"authorId":"2287861987","name":"Amanda Liu"},{"authorId":"1401885963","name":"Jonathan Ragan-Kelley"},{"authorId":"2364380098","name":"Joshua B. Tenenbaum"}],"citationStyles":{"bibtex":"@Inproceedings{Chandra2025GauguinDB,\n author = {Kartik Chandra and Amanda Liu and Jonathan Ragan-Kelley and Joshua B. Tenenbaum},\n booktitle = {Proceedings of the 2025 ACM SIGPLAN International Symposium on New Ideas, New Paradigms, and Reflections on Programming and Software},\n title = {Gauguin, Descartes, Bayes: A Diurnal Golem\u2019s Brain},\n year = {2025}\n}\n"},"paperId":"ff1831feefab441b2b01dc530b4ffb2f20d13008","title":"Gauguin, Descartes, Bayes: A Diurnal Golem\u2019s Brain","venue":"Proceedings of the 2025 ACM SIGPLAN International Symposium on New Ideas, New Paradigms, and Reflections on Programming and Software","year":2025},"contexts":["Consider the unexpected consequences of constructing a set that contains itself [Russell 1903], a machine that can simulate itself [Turing et al. 1936], or a compiler that can compile itself [Thompson 1984]."]},{"citingPaper":{"authors":[{"authorId":"2384362897","name":"Francesco Caravelli"},{"authorId":"145026953","name":"Jean-Charles Delvenne"}],"citationStyles":{"bibtex":"@Inproceedings{Caravelli2025AnalogAS,\n author = {Francesco Caravelli and Jean-Charles Delvenne},\n booktitle = {Journal of Physics: Complexity},\n title = {Analog and symbolic computation through the Koopman framework},\n year = {2025}\n}\n"},"paperId":"f6e82ade70909f21d63f5baaddbcc3e60a28b1cb","title":"Analog and symbolic computation through the Koopman framework","venue":"Journal of Physics: Complexity","year":2025},"contexts":["The foundations of computation theory were established in the 1930s with the equivalence of several intuitive notions of an \u201calgorithm\u201d: Church\u2019s \u03bb -calculus, Kleene\u2019s partial recursive functions, and Turing machines [1, 2]."]},{"citingPaper":{"authors":[{"authorId":"2307146067","name":"Hengyun Li"},{"authorId":"2068770052","name":"Jing Xi"},{"authorId":"2276314901","name":"Cathy H. C. Hsu"},{"authorId":"48317098","name":"Bruce X. B. Yu"},{"authorId":"2161631908","name":"X. Zheng"}],"citationStyles":{"bibtex":"@Inproceedings{Li2025GenerativeAI,\n author = {Hengyun Li and Jing Xi and Cathy H. C. Hsu and Bruce X. B. Yu and X. Zheng},\n booktitle = {Tourism Management},\n title = {Generative artificial intelligence in tourism management: An integrative review and roadmap for future research},\n year = {2025}\n}\n"},"paperId":"0fa48214d5db8698b07e4743518f214ebb48a24f","title":"Generative artificial intelligence in tourism management: An integrative review and roadmap for future research","venue":"Tourism Management","year":2025},"contexts":[]},{"citingPaper":{"authors":[{"authorId":"2256994240","name":"Holger Boche"},{"authorId":"35505035","name":"Andrea Grigorescu"},{"authorId":"2307454","name":"Rafael F. Schaefer"},{"authorId":"120463507","name":"H. Vincent Poor"}],"citationStyles":{"bibtex":"@Inproceedings{Boche2025AlgorithmicCO,\n author = {Holger Boche and Andrea Grigorescu and Rafael F. Schaefer and H. Vincent Poor},\n booktitle = {IEEE Transactions on Information Theory},\n title = {Algorithmic Computability of the Capacity of Additive Colored Gaussian Noise Channels},\n year = {2025}\n}\n"},"paperId":"4cfc4262c2f1a62eae88b7a4eb1cfdaf63e9a1c7","title":"Algorithmic Computability of the Capacity of Additive Colored Gaussian Noise Channels","venue":"IEEE Transactions on Information Theory","year":2025},"contexts":["The concept of computability, along with the notion of computable real numbers, were initially proposed by Turing in [31] and [32], where he introduced the idea of numbers that can be precisely determined by Turing machines.","To address algorithmic computability, we use the concept of a Turing machine [31], [32], [33], which is a mathematical model of an abstract machine that manipulates symbols on a strip of tape according to certain given rules."]}],"function":"lookup_citations","inputs":{"fields":"contexts,citationStyles,title,year,venue,authors","id":"CorpusId:73712","offset":"0"},"time":0.6917121410369873}
