Sprague-Grundy theory in bounded arithmetic
Satoru Kuroda
TL;DR
This paper formalizes Sprague-Grundy theory within bounded arithmetic and demonstrates that with Sprague-Grundy numbers, weak axioms can capture the complexity class PSPACE.
Contribution
It introduces a formalization of Sprague-Grundy theory in bounded arithmetic and links it to PSPACE complexity.
Findings
Sprague-Grundy numbers enable formal reasoning about combinatorial games.
Weak axioms combined with Sprague-Grundy theory capture PSPACE.
The formalization bridges combinatorial game theory and computational complexity.
Abstract
In this paper, we formalize Sprague-Grundy theory for combinatorial games in bounded arithmetic. We show that in the presence of Sprague-Grundy numbers, a fairly weak axioms capture PSPACE.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Artificial Intelligence in Games · Complexity and Algorithms in Graphs