Abstraction Refinement for Trace Inclusion of Infinite State Systems

TL;DR

This paper introduces a semi-algorithm for trace inclusion in data automata with infinite data domains, using abstraction refinement, and demonstrates its effectiveness through implementation and experiments.

Contribution

It presents a novel semi-algorithm for trace inclusion in data automata, combining abstraction refinement with soundness and completeness.

Findings

Prototype tool implementation shows promising results.

Effective handling of non-trivial examples.

Semi-algorithm is sound and complete, but not guaranteed to terminate.

Abstract

A \emph{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, but whose termination is not guaranteed. We have implemented our technique in a~prototype tool and show promising results on several non-trivial examples.