Which fragments of the interval temporal logic HS are tractable in model checking?

Since the 80s, model checking (MC) has been applied to the automatic verification of hardware/software systems. Point-based temporal logics, such as , , ⁎ , and the like, are commonly used in MC as the specification language; however, there are some inherently interval-based properties of computations, e.g., temporal aggregations and durations, that cannot be properly dealt with by these logics, as they model a state-by-state evolution of systems. Recently, an MC framework for the verification of interval-based properties of computations, based on Halpern and Shoham's interval temporal logic ( , for short) and its fragments, has been proposed and systematically investigated. In this paper, we focus on the boundaries that separate tractable and intractable fragments in MC. We first prove that MC for the logic of Allen's relations started-by and finished-by is provably intractable, being Expspace-hard. Such a lower bound immediately propagates to full . Then, in contrast, we show that other noteworthy fragments, i.e., the logic (resp., ) of Allen's relations meets, met-by, starts (resp., finishes), and started-by (resp., finished-by), are well-behaved, and turn out to have the same complexity as (Pspace-complete). Halfway are the fragments and , whose Expspace membership and Pspace hardness are already known. Here, we give an original proof of Expspace membership, that substantially simplifies the complexity of the constructions previously used for such a result. Contraction techniques—suitably tailored to each fragment—are at the heart of our results, enabling us to prove a pair of remarkable small-model properties

Satisfiability and Model Checking for the Logic of Sub-Intervals under the Homogeneity Assumption

The expressive power of interval temporal logics (ITLs) makes them really fascinating, and one of the most natural choices as specification and planning language. However, for a long time, due to 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 featuring 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). First we prove that the satisfiability problem for D, over finite linear orders, is PSPACE-complete; then we show that its model checking problem, over finite Kripke structures, is PSPACE-complete as well. The paper enrich the set of tractable interval temporal logics with a meaningful representative.Comment: arXiv admin note: text overlap with arXiv:1901.0388

PSPACE-completeness of the temporal logic of sub-intervals and suffixes

In this paper, we prove PSPACE-completeness of the finite satisfiability and model checking problems for the fragment of Halpern and Shoham interval logic with modality 〈E〉, for the “suffix” relation on pairs of intervals, and modality 〈D〉, for the “sub-interval” relation, under the homogeneity assumption. The result significantly improves the EXPSPACE upper bound recently established for the same fragment, and proves the rather surprising fact that the complexity of the considered problems does not change when we add either the modality for suffixes (〈E〉) or, symmetrically, the modality for prefixes (〈B〉) to the logic of sub-intervals (featuring only 〈D〉)