Abstraction refinement and antichains for trace inclusion of infinite state systems

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 duri...

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Bibliographic Details
Published in:Formal methods in system design 2020-11, Vol.55 (3), p.137-170
Main Authors: Holík, Lukáš, Iosif, Radu, Rogalewicz, Adam, Vojnar, Tomáš
Format: Article
Language:English
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
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Summary: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.
ISSN:0925-9856
1572-8102
DOI:10.1007/s10703-020-00345-1