Abstraction refinement and antichains for trace inclusion of infinite state systems

• Published in: Formal methods in system design Vol. 55; no. 3; pp. 137 - 170
• Main Authors: Holík, Lukáš, Iosif, Radu, Rogalewicz, Adam, Vojnar, Tomáš
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2020; Springer Verlag
• Subjects: CAE) and Design; Circuits and Systems; Computer Science; Computer-Aided Engineering (CAD; Electrical Engineering; Engineering; Formal Languages and Automata Theory; Software Engineering/Programming and Operating Systems; Trace inclusion; Interpolation; CEGAR; Simulation relations; Data automata; Generic register automata; Antichains
• ISSN: 0925-9856; 1572-8102; 1572-8102
• DOI: 10.1007/s10703-020-00345-1

A generic register automaton is a finite automaton equipped with variables (which may be viewed as counters or, more generally, registers) ranging over infinite data domains. A trace of a generic register automaton is an alternating sequence of alphabet symbols and values taken by the variables 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 a combination of abstraction refinement and antichains, which is proved to be sound and complete, but whose termination is not guaranteed. Moreover, we further enhance the proposed algorithm by exploiting a concept of data simulations, i.e., simulation relations aware of the data associated with the words. We have implemented our technique in a prototype tool and show promising results on multiple non-trivial examples.