Journal ArticleDOI
Some undecidable determined games
TLDR
In this paper, the authors obtained similar theorems of this type but the winning conditions are extremely simple relations (polynomial equations) and the winning strategies are computable.Abstract:
Computing machines using algorithms play games and even learn to play games. However, the inherent finiteness properties of algorithms impose limitations on the game playing abilities of machines. M. Rabin illustrated this limitation in 1957 by constructing a two-person win-lose game with decidable rules but no computable winning strategies. Rabin's game was of the type where two players take turns choosing integers to satisfy some decidable but very complicated winning condition. In the present paper we obtain similar theorems of this type but the winning conditions are extremely simple relations (polynomial equations). Specific examples are given.read more
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Combinatorial games: Selected bibliography with a succinct gourmet introduction.
TL;DR: The family of combinatorial games consists of two-player games with perfect information, no hidden information as in some card games, no chance moves and outcome restricted to (lose, win), (tie, tie) and (draw, draw) for the two players who move alternately.
Journal ArticleDOI
Complexity, appeal and challenges of combinatorial games
TL;DR: A definition of the tractability, polynomiality and efficiency of subsets of games, and the nature of the subclasses PlayGames and MathGames.
Posted Content
Undecidable problems: a sampler
TL;DR: A survey of undecidable decision problems arising in various branches of mathemat- ics is given in this paper, where two senses in which undecidability is used are discussed.
Combinatorial Games: selected Bibliography with a Succinct Gourmet Introduction
TL;DR: The combinatorial games as mentioned in this paper are a family of games with perfect information (no hidden information as in some card games), no chance moves (no dice) and outcome restricted to (lose, win), (tie, tie) and (draw, draw) for the two players who move alternately.
Journal ArticleDOI
Combinatorial Game Theory Foundations Applied to Digraph Kernels
TL;DR: Game theory tools are constructed concerning strategies in the presence of draw positions, and it is shown that G can be decomposed, in O(|E|) time, into two induced subgraphs, which has no kernel if and only if G_2 has none.
References
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Journal ArticleDOI
Theory of Recursive Functions and Effective Computability.
Solomon Feferman,Hartley Rogers +1 more
TL;DR: Central concerns of the book are related theories of recursively enumerable sets, of degree of un-solvability and turing degrees in particular and generalizations of recursion theory.
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Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I
Journal ArticleDOI
Recursively enumerable sets of positive integers and their decision problems
TL;DR: The notion of recursive functions of positive integers has been studied in the context of symbolic logic as discussed by the authors, and it has been shown that such a concept admits of development into a mathematical theory much as the group concept has been developed into a theory of groups.