文章基本信息

标题：BÃ¼chi Complementation and Size-Change Termination
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作者：Seth Fogarty ; Moshe Vardi
期刊名称：Logical Methods in Computer Science
印刷版ISSN：1860-5974
电子版ISSN：1860-5974
出版年度：2012
卷号：8
期号：1
页码：1
DOI：10.2168/LMCS-8(1:13)2012
出版社：Technical University of Braunschweig
摘要：We compare tools for complementing nondeterministic Büchi automata with a recent termination-analysis algorithm. Complementation of Büchi automata is a key step in program verification. Early constructions using a Ramsey-based argument have been supplanted by rank-based constructions with exponentially better bounds. In 2001 Lee et al. presented the size-change termination (SCT) problem, along with both a reduction to Büchi automata and a Ramsey-based algorithm. The Ramsey-based algorithm was presented as a more practical alternative to the automata-theoretic approach, but strongly resembles the initial complementation constructions for Büchi automata. We prove that the SCT algorithm is a specialized realization of the Ramsey-based complementation construction. To do so, we extend the Ramsey-based complementation construction to provide a containment-testing algorithm. Surprisingly, empirical analysis suggests that despite the massive gap in worst-case complexity, Ramsey-based approaches are superior over the domain of SCT problems. Upon further analysis we discover an interesting property of the problem space that both explains this result and provides a chance to improve rank-based tools. With these improvements, we show that theoretical gains in efficiency of the rank-based approach are mirrored in empirical performance.
其他关键词：B¨uchi Complementation, Model Checking, Formal Verification, Automata, B¨uchi Automata