Fogarty, Seth and Vardi, Moshe Y. - B\"uchi Complementation and Size-Change Termination

lmcs:1178 - Logical Methods in Computer Science, February 27, 2012, Volume 8, Issue 1
B\"uchi Complementation and Size-Change Termination

Authors: Fogarty, Seth and Vardi, Moshe Y.

We compare tools for complementing nondeterministic B\"uchi automata with a recent termination-analysis algorithm. Complementation of B\"uchi 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 B\"uchi 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 B\"uchi 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.

Source :
DOI : 10.2168/LMCS-8(1:13)2012
Volume: Volume 8, Issue 1
Published on: February 27, 2012
Submitted on: December 2, 2011
Keywords: Computer Science - Formal Languages and Automata Theory,D.2.4


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