TIFRMetric Temporal Logic MTL[ U I , S I ] is one of the most studied real time logics. It exhibits considerable diversity in expressiveness and decidability properties based on the permitted set of modalities and the nature of time interval constraints I. Henzinger et al., in their seminal paper showed that the non-punctual fragment of MTL called MITL is decidable. In this paper, we sharpen this decidability result by showing that the partially punctual fragment of MTL (denoted PMTL) is decidable over strictly monotonic finite point wise time. In this fragment, we allow either punctual future modalities, or punctual past modalities, but never both together. We give two satisfiability preserving reductions from PMTL to the decidable logic MTL[ U I ]. The first reduction uses simple projections, while the second reduction uses a novel technique of temporal projections with oversampling. We study the trade-off between the two reductions: while the second reduction allows the introduction of extra action points in the underlying model, the equisatisfiable MTL[ U I ] formula obtained is exponentially succinct than the one obtained via the first reduction, where no oversampling of the underlying model is needed. We also show that PMTL is strictly more expressive than the fragments MTL[ U I , S] and MTL[ U, S I ].

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Self-triggered control (STC) is a sample-and-hold control method aimed at reducing communications in networkedcontrol systems; however, existing STC mechanisms often maximize how late the next sample is, thus not optimizing sampling performance in the long-term. In this work, we devise a method to construct self-triggered policies that provide nearmaximal average inter-sample time (AIST) while respecting given control performance constraints. To achieve this, we rely on finite-state abstractions of a reference event-triggered control, while also allowing earlier samples. These early triggers constitute controllable actions of the abstraction, for which an AIST-maximizing strategy can be obtained by solving a meanpayoff game. We provide optimality bounds, and how to further improve them through abstraction refinement techniques.

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Metric Temporal Logic, MTL pw [UI , SI ], is amongst the most studied real-time logics. It exhibits considerable diversity in expressiveness and decidability properties based on the permitted set of modalities and the nature of time interval constraints I. In this paper, we sharpen the decidability results by showing that the satisfiability of MTL pw [ UI , SNS] (where N S denotes non-singular intervals) is also decidable over finite pointwise strictly monotonic time. We give a satisfiability preserving reduction from MTL pw [ UI , SNS] to the decidable logic MTL pw [ UI ] of Ouaknine and Worrell using a novel technique of temporal projections with oversampling. We also investigate the decidability of unary fragment MTL pw [♦I , ♦− I ] and we compare the expressive powers of some of these fragments.