Mixed Transition Systems Revisited

Partial models support abstract model-checking of complex temporal properties by combining both over- and under-approximating abstractions into a single model. Over the years, three families of such modeling formalisms have emerged, represented by Kripke Modal Transition Systems (KMTSs), with restrictions on necessary and possible behaviors, Mixed Transition Systems (MixTSs), with relaxation on these restrictions, and Generalized Kripke MTSs (GKMTSs), with hyper-transitions, respectively. In this paper, we compare the three families w.r.t. their expressive power (i.e., what can be modeled, what abstraction can be captured), and the cost and precision of model-checking. We show that these families have the same expressive power (but do differ in succinctness), whereas GKMTSs are more precise (i.e, can establish more properties) for model-checking than the other two families. However, the use of GKMTSs in practice has been hampered by the difficulty of encoding them symbolically. We address this problem by developing a new semantics for temporal logic of partial models that makes the MixTS family as precise for model-checking as the GKMTS family. The outcome is a symbolic model-checking algorithm that combines the efficient symbolic encoding of MixTSs with the model-checking precision of GKMTSs. Our preliminary experiments indicate that the new algorithm is a good match for predicate-abstraction-based model-checkers.