Game arguments in computability theory and algorithmic information theory
Andrej Muchnik, Alexander Shen, Mikhail Vyugin
TL;DR
This paper demonstrates how game-theoretic arguments can be applied to key problems in computability and algorithmic information theory, including theorems like Friedberg's and Epstein-Levin's.
Contribution
It introduces a novel perspective by using game-theoretic methods to prove and analyze fundamental results in the field.
Findings
Game-theoretic proofs of classical theorems
Insights into complexity gaps and total conditional complexity
New unpublished results by researchers
Abstract
We provide some examples showing how game-theoretic arguments can be used in computability theory and algorithmic information theory: unique numbering theorem (Friedberg), the gap between conditional complexity and total conditional complexity, Epstein--Levin theorem and some (yet unpublished) result of Muchnik and Vyugin
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Logic, Reasoning, and Knowledge · Algorithms and Data Compression