Bridging the gap between fair simulation and trace inclusion

Authors:
Yonit Kesten;Nir Piterman;Amir Pnueli
Affiliations:
Department of Communication Systems Engineering, Ben Gurion University, Beer-Sheva, Israel;Department of Applied Mathematics and Computer Science, Weizmann Institute of Science, Rehovot 76100, Israel;Department of Applied Mathematics and Computer Science, Weizmann Institute of Science, Rehovot 76100, Israel
Venue:
Information and Computation
Year:
2005

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Abstract

The paper considers the problem of checking abstraction between two finite-state fair discrete systems. In automata-theoretic terms this is trace inclusion between two nondeterministic Streett automata. We propose to reduce this problem to an algorithm for checking fair simulation between two generalized Buchi automata. For solving this question we present a new triply nested @m-calculus formula which can be implemented by symbolic methods. We then show that every trace inclusion of this type can be solved by fair simulation, provided we augment the concrete system (the contained automaton) by an appropriate 'non-constraining' automaton. This establishes that fair simulation offers a complete method for checking trace inclusion for finite-state systems. We illustrate the feasibility of the approach by algorithmically checking abstraction between finite state systems whose abstraction could only be verified by deductive methods up to now.