How to Order Vertices for Distributed LTL Model-Checking Based on Accepting Predecessors

Distributed automata-based LTL model-checking relies on algorithms for finding accepting cycles in a Büchi automaton. The approach to distributed accepting cycle detection as presented in [L. Brim, I. Černá, P. Moravec, J. Šimša. Accepting Predecessors are Better than Back Edges in Distributed LTL Model-Checking. In Formal Methods in Computer-Aided Design (FMCAD'04), volume 3312 of LNCS, pages 352–366. Springer, 2004] is based on maximal accepting predecessors. The ordering of accepting states (hence the maximality) is one of the main factors affecting the overall complexity of model-checking as an imperfect ordering can enforce numerous re-explorations of the automaton. This paper addresses the problem of finding an optimal ordering, proves its hardness, and gives several heuristics for finding an optimal ordering in the distributed environment. We compare the heuristics both theoretically and experimentally to find out which of these work well.     

A power-set construction for reducing Büchi automata to non-determinism degree two

Büchi automata are finite automata that accept languages of infinitely long strings, so-called ω-languages. It is well known that, unlike in the finite-string case, deterministic and non-deterministic Büchi automata accept different ω-language classes, i.e., that determination of a non-deterministic Büchi automaton using the classical power-set construction will yield in general a deterministic Büchi automaton which accepts a superset of the ω-language accepted by the given non-deterministic automaton.In this paper, a power-set construction to a given Büchi automaton is presented, which reduces the degree of non-determinism of the automaton to at most two, meaning that to each state and input symbol, there exist at most two distinct successor states. The constructed Büchi automaton of non-determinism degree two and the given Büchi automaton of arbitrary non-determinism degree will accept the same ω-language.