B\"uchi Complementation and Size-Change Termination

TL;DR

This paper compares B"uchi automata complementation methods with a size-change termination algorithm, revealing that Ramsey-based approaches outperform rank-based methods in practice for SCT problems, despite worse theoretical bounds.

Contribution

It demonstrates that the size-change termination algorithm is a specialized form of Ramsey-based B"uchi automata complementation, and improves rank-based tools based on new insights.

Findings

Ramsey-based approaches outperform rank-based methods on SCT problems.

Empirical analysis confirms practical superiority despite theoretical complexity.

Enhanced rank-based tools show improved empirical performance.

Abstract

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.