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In this article, we introduce and investigate an extension of Halpern and Shoham’s interval temporal logic HS for the specification and verification of branching-time context-free requirements of pushdown systems under a state-based semantics over Kripke structures enforcing visibility of the pushdown operations. The proposed logic, called nested BHS , supports branching-time both in the past and in the future and is able to express non-regular properties of linear and branching behaviours of procedural contexts in a natural way. It strictly subsumes well-known linear time context-free extensions of LTL such as CaRet [ 4 ] and NWTL [ 2 ]. The main result is the decidability of the visibly pushdown model-checking problem against nested BHS . The proof exploits a non-trivial automata-theoretic construction.

The edge-cloud collaboration network is promising to support complex requirements with temporal constraints, where a requirement can be achieved through the composition of computation-demanding and delay-sensitive services. In this setting, most services should be optimally configured at the network edge, in order to decreasing service response latency and reducing network resource consumption. To address this challenge, this paper proposes an optimal service configuration mechanism, where temporal constraints between services are mined from event logs through our temporal interval discovery mechanism. Service configuration is formulated as a constrained multi-objective optimization problem, which is solved by our improved non-dominated sorting genetic algorithm II. Extensive experiments are conducted, and evaluation results demonstrate that our approach can find the close-to-optimal service configuration in comparison with the state-of-the-art techniques in terms of delay sensitivity and energy efficiency, especially when edge nodes can co-host a relatively large number of services.

Model checking for Halpern and Shoham's interval temporal logic HS has been recently investigated in a systematic way, and it is known to be decidable under three distinct semantics. Here, we focus on the trace-based semantics, where the infinite execution paths (traces) of the given (finite) Kripke structure are the main semantic entities. In this setting, each finite infix of a trace is interpreted as an interval, and a proposition holds over an interval if and only if it holds over each component state (homogeneity assumption). In this paper, we introduce a quantitative extension of HS over traces, called parametric HS (PHS). The novel logic allows to express parametric timing constraints on the duration (length) of the intervals. We show that checking the existence of a parameter valuation for which a Kripke structure satisfies a PHS formula (model checking), or a PHS formula admits a trace as a model under the homogeneity assumption (satisfiability) is decidable. Moreover, we identify a fragment of PHS which subsumes parametric LTL and for which model checking and satisfiability are shown to be EXPSPACE-complete., In Proceedings GandALF 2022, arXiv:2209.09333

Model checking (MC) for Halpern and Shoham’s interval temporal logic HS has been recently investigated in a systematic way, and it is known to be decidable under three distinct semantics (state-based, trace-based and tree-based semantics), all of them assuming homogeneity in the propositional valuation. Here, we focus on the trace-based semantics, where the main semantic entities are the infinite execution paths (traces) of the given Kripke structure. We introduce a quantitative extension of HS over traces, called Difference HS (DHS), allowing one to express timing constraints on the difference among interval lengths (durations). We show that MC and satisfiability of full DHS are in general undecidable, so, we investigate the decidability border for these problems by considering natural syntactical fragments of DHS. In particular, we identify a maximal decidable fragment DHS_{simple} of DHS proving in addition that the considered problems for this fragment are at least 2Expspace-hard. Moreover, by exploiting new results on linear-time hybrid logics, we show that for an equally expressive fragment of DHS_{simple}, the problems are Expspace-complete. Finally, we provide a characterization of HS over traces by means of the one-variable fragment of a novel hybrid logic., LIPIcs, Vol. 247, 29th International Symposium on Temporal Representation and Reasoning (TIME 2022), pages 11:1-11:16

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., Comment: arXiv admin note: text overlap with arXiv:1901.03880