Utilizing symmetry when model-checking under fairness assumptions: an automata-theoretic approach

One useful technique for combating the state explosion problem is to exploit symmetry when performing temporal logic model checking. In previous work it is shown how, using some basic notions of group theory, symmetry may be exploited for the full range of correctness properties expressible in the very expressive temporal logic CTL*. Surprisingly, while fairness properties are readily expressible in CTL*, these methods are not powerful enough to admit any amelioration of state explosion, when fairness assumptions are involved. We show that it is nonetheless possible to handle fairness efficiently by trading some group theory for automata theory. Our automata-theoretic approach depends on detecting fair paths subtly encoded in a quotient structure whose arcs are annotated with permutations, by using a threaded structure that reflects coordinate shifts caused by the permutations.