Simulation Subsumption in Ramsey-Based Büchi Automata Universality and Inclusion Testing

Abstract

There are two main classes of methods for checking universality and language inclusion of Büchi-automata: Rank-based methods and Ramsey-based methods. While rank-based methods have a better worst-case complexity, Ramsey-based methods have been shown to be quite competitive in practice [9, 8]. It was shown in [9] (for universality checking) that a simple subsumption technique, which avoids exploration of certain cases, greatly improves the performance of the Ramsey-based method. Here, we present a much more general subsumption technique for the Ramsey-based method, which is based on using simulation preorder on the states of the Büchi-automata. This technique applies to both universality and inclusion checking, yielding a substantial performance gain over the previous simple subsumption approach of [9].

Advanced Ramsey-Based Büchi Automata Inclusion Testing

“…We have compared the performance of the new algorithm with the one in [1] (which only uses supergraphs, not metagraphs, and subsumption and minimization based on forward simulation on A and on B), and found it better on average, and, in particular, on difficult instances where the inclusion holds. Below, we present a condensed version of the results.…”

“…We now present a relaxed DGT proposed in [1], which we further improve below. The idea is to weaken the properness condition in order to allow more pairs of supergraphs to be eligible for LFT on their graph part.…”

“…Definition 4. (adapted from [1]) A pair of edges ( p, a, q , r, b, s ) is weakly proper iff p ∈ I A , r f q, r f s, and b = 1, 3 and a pair of supergraphs (g = x, g , h = y, h ) is weakly proper when (x, y) is weakly proper. Supergraphs g, h pass the relaxed double graph test, denoted RDGT(g, h), iff whenever (g, h) is weakly proper, then LFT(g, h).…”

“…This is safe in the sense that if a subsumed supergraph can yield a counterexample to language inclusion, then also the subsuming one can yield a counterexample. We present an improved version of the subsumption from [1]. The new version uses both f and b on the B part of supergraphs instead of f only.…”

“…The new version uses both f and b on the B part of supergraphs instead of f only. This allows us to discard significantly more supergraphs than in [1], as illustrated in Section 8.…”