Abstraction Refinement and Antichains for Trace Inclusion of Infinite State Systems

Abstract

A data automaton is a finite automaton equipped with variables counters or registers ranging over infinite data domains. A trace of a data automaton is an alternating sequence of alphabet symbols and values taken by the counters during an execution of the automaton. The problem addressed in this paper is the inclusion between the sets of traces data languages recognized by such automata. Since the problem is undecidable in general, we give a semi-algorithm based on abstraction refinement, which is proved to be sound and complete modulo termination. Due to the undecidability of the trace inclusion problem, our procedure is not guaranteed to terminate. We have implemented our technique in ai¾?prototype tool and show promising results on several non-trivial examples.