Multi-core Emptiness Checking of Timed Büchi Automata Using Inclusion Abstraction

Abstract

Abstract. This paper contributes to the multi-core model checking of timed automata (TA) with respect to liveness properties, by investigating checking of TA Büchi emptiness under the very coarse inclusion abstraction or zone subsumption, an open problem in this field. We show that in general Büchi emptiness is not preserved under this abstraction, but some other structural properties are preserved. Based on those, we propose a variation of the classical nested depth-first search (ndfs) algorithm that exploits subsumption. In addition, we extend the multi-core cndfs algorithm with subsumption, providing the first parallel LTL model checking algorithm for timed automata. The algorithms are implemented in LTSmin, and experimental evaluations show the effectiveness and scalability of both contributions: subsumption halves the number of states in the real-world FDDI case study, and the multi-core algorithm yields speedups of up to 40 using 48 cores.

Topics in Theoretical Computer Science

“…We introduced a parallel version of this algorithm [9], despite the fact that Depth-First Search is hard to parallelize. Our multi-core implementation is compatible with important state space reduction techniques, in particular state compression and partial-order reduction [11,15] and generalizes to timed automata [13].…”

LTSmin: High-Performance Language-Independent Model Checking

“…A new LTL model checking algorithm with subsumption [36] is also supported, by extending the multi-core cndfs algorithm (see Section 5.1).…”

Robust Controller Synthesis in Timed Büchi Automata: A Symbolic Approach

“…Thus, the role of the controller is to choose transitions and delays. This problem has been studied numerously in the exact setting [13][14][15]17,19,27,28]. In the context of robustness, this strategy should be tolerant to small perturbations of the delays.…”

“…Our algorithm can be understood as an adaptation to the robustness setting of the standard algorithm for Büchi acceptance in timed automata [17]. This algorithm looks for an accepting lasso using a double depth-first search.…”