Abstract
The expressive power of interval temporal logics (ITLs) makes them one of the most natural choices in a number of application domains, ranging from the specification and verification of complex reactive systems to automated planning. However, for a long time, because of their high computational complexity, they were considered not suitable for practical purposes. The recent discovery of several computationally well-behaved ITLs has finally changed the scenario. In this paper, we investigate the finite satisfiability and model checking problems for the ITL D, that has a single modality for the sub-interval relation, under the homogeneity assumption (that constrains a proposition letter to hold over an interval if and only if it holds over all its points). We first prove that the satisfiability problem for D, over finite linear orders, is PSPACE-complete, and then we show that the same holds for its model checking problem, over finite Kripke structures. In such a way, we enrich the set of tractable interval temporal logics with a new meaningful representative.
Highlights
For a long time, interval temporal logics (ITLs) were considered an attractive, but impractical, alternative to standard point-based ones
We investigate the finite satisfiability and model checking problems for the ITL D, that has a single modality for the sub-interval relation, under the homogeneity assumption
We first prove that the satisfiability problem for D, over finite linear orders, is PSPACE-complete, and we show that the same holds for its model checking problem, over finite Kripke structures
Summary
Interval temporal logics (ITLs) were considered an attractive, but impractical, alternative to standard point-based ones. We show that the decidability of the satisfiability problem for D over the class of finite linear orders can be recovered by assuming homogeneity (the homogeneity assumption constrains a proposition letter to hold over an interval if and only if it holds over all its constituent points). The exact complexity of the model checking problem for BE, over finite Kripke structures, under the homogeneity assumption, is still unknown and it is a difficult open question whether it can be solved elementarily. Satisfiability for the temporal logic of reflexive subintervals over the class of finite linear orders is decidable and PSPACE-complete [MPS10]. Conclusions summarize the work done and outline future research directions
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