Mathematical Structures in Computer Science. A Journal in the Applications of Categorical, Algebraic and Geometric Methods in Computer Science, 2012, том 22, выпуск 5, страницы 729–751 DOI: https://doi.org/10.1017/S0960129511000508(Mi mscs1)
Эта публикация цитируется в 13 научных статьях (всего в 13 статьях)
Renormalisation and computation II: time cut-off and the Halting problem
Аннотация:
This is the second instalment in the project initiated in Manin (2012). In the first Part, we argued that both the philosophy and technique of perturbative renormalisation in quantum field theory could be meaningfully transplanted to the theory of computation, and sketched several contexts supporting this view.
In this second part, we address some of the issues raised in Manin (2012) and develop them further in three contexts: a categorification of the algorithmic computations; time cut-off and anytime algorithms; and, finally, a Hopf algebra renormalisation of the Halting Problem.
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Тип публикации:
Статья
Язык публикации: английский
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/mscs1
Эта публикация цитируется в следующих 13 статьяx:
Ali Shojaei-Fard, “Renormalization bi-Heyting algebra”, Journal of Applied Analysis, 2025
S. V. Kozyrev, “Transformers as a Physical Model in AI”, Lobachevskii J Math, 45:2 (2024), 710
Ali Shojaei-Fard, “Non-perturbative graph languages, halting problem and complexity”, Forum Mathematicum, 2022
Ali Shojaei-Fard, “FROM DYSON–SCHWINGER EQUATIONS TO QUANTUM ENTANGLEMENT”, J Math Sci, 266:6 (2022), 892
Cristian S. Calude, Monica Dumitrescu, “A statistical anytime algorithm for the Halting Problem”, COM, 9:2 (2020), 155
Cristian S. Calude, Monica Dumitrescu, Benedikt Löwe, “A probabilistic anytime algorithm for the halting problem”, COM, 7:2-3 (2018), 259
Ali Shojaei-Fard, “A new perspective on intermediate algorithms via the Riemann–Hilbert correspondence”, Quantum Stud.: Math. Found., 4:2 (2017), 127
Cristian S. Calude, Damien Desfontaines, “Anytime Algorithms for Non-Ending Computations”, Int. J. Found. Comput. Sci., 26:04 (2015), 465
Yuri I. Manin, Emergence, Complexity and Computation, 14, ISCS 2014: Interdisciplinary Symposium on Complex Systems, 2015, 3
Matilde Marcolli, Nicolas Tedeschi, “Entropy algebras and Birkhoff factorization”, Journal of Geometry and Physics, 97 (2015), 243
Matilde Marcolli, Lecture Notes in Computer Science, 9389, Geometric Science of Information, 2015, 271
Y I Manin, “Complexity vs energy: theory of computation and theoretical physics”, J. Phys.: Conf. Ser., 532 (2014), 012018
Ю. И. Манин, “Закон Ципфа и вероятностные распределения Левина”, Функц. анализ и его прил., 48:2 (2014), 51–66; Yu. I. Manin, “Zipf's Law and L. Levin Probability Distributions”, Funct. Anal. Appl., 48:2 (2014), 116–127
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