Problem
Research questions and friction points this paper is trying to address.
Büchi automaton
complementation
congruence-based
Ramsey theorem
From Ramsey-Based to Congruence-Based Constructions for B\"uchi Complementation
🤖 AI Summary
本文讨论了从基于Ramsey理论到基于同余类方法的Büchi自动机补集构造，提出使用同余类方法可以简化证明并改进构造。
📝 Abstract
The very first construction by J. Richard B\"uchi himself for complementing a B\"uchi automaton relies on a fundamental lemma about the division of an arbitrary infinite word into consecutive finite words, which was cleanly proven by invoking a specialized theorem of Ramsey. For that reason, constructions of similar nature have subsequently been labeled as Ramsey-based. Nevertheless, it suffices to have a weaker form of the lemma where the finite words come from a finite number of congruence classes, rather than arbitrary classes, that form a partition of the set of all finite words. The weaker lemma, with support of nicer properties from a congruence, can be proven without Ramsey's theorem. A commonly adopted improvement on such complementation constructions also requires the working of a congruence. This paper recounts the history and reviews using more contemporary terminology wherever possible the relevant concepts and results, to advocate renaming of Ramsey-based constructions as congruence-based constructions.
Innovation
Methods, ideas, or system contributions that make the work stand out.
congruence-based
Büchi complementation
weaker lemma
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