Abstract
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. It is a way to relate the set-theoretic definition of a function to the program that computes it. The approach, though very preliminary, may show how to improve a given algorithm.
Partially supported by French “Agence Nationale de la Recherche” under the project EQINOCS (ANR-11-BS02-004) and by Government of the Russian Federation, Grant 074-U01.
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References
Floridi, L.: Semantic conceptions of information. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy, Spring 2013 edn. (2013)
Gurevich, Y.: Evolving algebra 1993: lipari guide. In: Börger, E. (ed.) Specification and Validation Methods, pp. 9–93. Oxford University Press, Oxford (1995)
Kolmogorov, A.N., Tikhomirov, V.M.: \(\varepsilon \)-entropy and \(\varepsilon \)-capacity of sets in function spaces. Uspekhi Mat. Nauk 14(8(2(86))), 3–86 (1959). (in Russian) In: Selected Works of A.N. Kolmogorov: Volume III: Information Theory and the Theory of Algorithms (Mathematics and its Applications). Kluwer Academic Publishers (1992)
Martin, N.F.G., England, J.W.: Mathematical Theory of Entropy. Encyclopedia of Mathematics and its Applications, vol. 12. Addison-Wesley, Boston (1981)
Slissenko, A.: On entropic convergence of algorithms in terms of domain partitions. Technical report, University Paris-East Créteil, Laboratory for Algorithmics, Complexity and Logic (LACL) (2016). http://arxiv.org/abs/1605.01519
Acknowledgements
I am thankful to Eugène Asarine and Vladimir Lifschitz for discussions and comments that were stimulating, and to anonymous referee for very useful remarks.
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Slissenko, A. (2020). On Entropic Convergence of Algorithms. In: Blass, A., Cégielski, P., Dershowitz, N., Droste, M., Finkbeiner, B. (eds) Fields of Logic and Computation III. Lecture Notes in Computer Science(), vol 12180. Springer, Cham. https://doi.org/10.1007/978-3-030-48006-6_19
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