The paper considers the problem of checking abstraction between two finite-state \emm{fair discrete systems} (\fds). 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 B\"{u}chi automata. For solving this question we present a new triply nested \${\mu}-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 %nir1 contained automaton) by an appropriate `non-constraining' automaton. This %contained automaton) by appropriate auxiliary variables. 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.
@article{KPP03,
author = "Y. Kesten and N. Piterman and A. Pnueli",
title = "Bridging the Gap between Fair Simulation and Trace
Containment",
journal = "Information and Computation",
year = 2005,
}