Efficient Patterns for Model Checking Partial State Spaces in CTL ∩ LTL

Abstract

Compositional model checks of partial Kripke structures are efficient but incomplete as they may fail to recognize that all implementations satisfy the checked property. But if a property holds for such checks, it will hold in all implementations. Such checks are therefore under-approximations. In this paper we determine for which popular specification patterns, documented at a communityled pattern repository, this under-approximation is precise in that the converse relationship holds as well for all model checks. We find that many such patterns are indeed precise. Those that aren't lose precision because of a sole propositional atom in mixed polarity. Hence we can compute, with linear blowup only, a semantic minimization in the same temporal logic whose efficient check renders the precise result for the original imprecise pattern. Thus precision can be secured for all patterns at low cost.