Propositional temporal interval logic is PSPACE complete

Abstract

We define a notion of πα equivalence of two execution sequences, where π is the set of variables shared between the two sequences and α is a set of variables disjoint from π appearing in only one of them. We call the set of variables α as auxiliary variables. We extend the notion of πα equivalence to formulas in temporal logics, and there by to classes of temporal logics. Under such a notion, we provide sound and complete translation scheme from Propositional Temporal Interval Logic(PTIL) to Linear Time Propositional Temporal Logic (PTL). We do so via the introduction of a chop operator into PTL. The PTIL that we consider is of Swartz, Melliar-Smith variety[13]. The translations that we give are Polynomial in space and time. Together with the results of Sistla and Clarke[14], we conclude that the satisfiability problem for PTIL is PSpace. Known decision procedures for PTIL are exponential in space[9]. The translations provide a means with which synchronization skeletons could be synthesized from specifications given in PTIL. We have constructed a prolog based prototype implementation of the synthesizer.