Büchi Complementation and Size-Change Termination

We compare tools for complementing nondeterministic Buchi automata with a recent termination-analysis algorithm. Complementation of Buchi 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 Buchi automata and a Ramsey-based algorithm. This algorithm strongly resembles the initial complementation constructions for Buchi automata. We prove that the SCT algorithm is a specialized realization of the Ramsey-based complementation construction. Surprisingly, empirical analysis suggests 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 are mirrored in empirical performance.

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