We present a new heuristic for on-the-fly enumerative invariant verification. The heuristic is based on a construct for temporal scaling, called next, that compresses a sequence of transitions leading to a given target set into a single metatransition. First, we give an on-the-fly algorithm to search a process expression built using the constructs of hiding, parallel composition, and temporal scaling. Second, we show that as long the target set Theta of transitions includes all transitions that access variables shared with the environment, the process next Theta for P and P are equivalent according to the weak-simulation equivalence. As a result, to search the product of given processes, we can cluster processes into groups with as little communication among them as possible, and compose the groups only after applying appropriate hiding and temporal scaling operators. Applying this process recursively gives an expression that has multiple nested applications of next, and has potentially much fewer states than the original product. We report on an implementation, and show significant reductions for a tree-structured parity computer and a ring-structured leader-election protocol.
In Proceedings of the Tenth International Conference on Concurrency Theory (CONCUR'99), Lecture Notes in Computer Science 1664, Springer-Verlag, pp. 98--113, 1999.