On the Satisfiability of Metric Temporal Logics over the Reals

We show that there is a satisfiability-preserving translation of QTL formulae interpreted over finitely variable behaviors into formulae of the CLTL-overclocks logic. The satisfiability of CLTL-over-clocks can be determined through a suitable encoding into the input logics of SMT solvers, so it constitutes an effective decision procedure for QTL. Although decision procedures for determining satisfiability of QTL (and for the expressively equivalent logics MITL and QMLO) already exist, the automata-based techniques they employ appear to be very difficult to realize in practice, and, to the best of our knowledge, no implementation currently exists for them. A prototype tool for QTL based on the encoding presented here has, instead, been implemented and is publicly available

On the Satisfiability of Metric Temporal Logics over the Reals

We show that there is a satisfiability-preserving translation of QTL formulae interpreted over finitely variable behaviors into formulae of the CLTL-overclocks logic. The satisfiability of CLTL-over-clocks can be determined through a suitable encoding into the input logics of SMT solvers, so it constitutes an effective decision procedure for QTL. Although decision procedures for determining satisfiability of QTL (and for the expressively equivalent logics MITL and QMLO) already exist, the automata-based techniques they employ appear to be very difficult to realize in practice, and, to the best of our knowledge, no implementation currently exists for them. A prototype tool for QTL based on the encoding presented here has, instead, been implemented and is publicly available

A Logical Characterization of Timed (non-)Regular Languages

CLTLoc (Constraint LTL over clocks) is a quantifier-free extension of LTL allowing variables behaving like clocks over real numbers. CLTLoc is in PSPACE [9] and its satisfiability can polynomially be reduced to a SMT problem, allowing a feasible implementation of a decision procedure. We used CLTLoc to capture the semantics of metric temporal logics over continuous time, such as Metric Interval Temporal Logic (MITL), resulting in the first successful implementation of a tool for checking MITL satisfiability [7]. In this paper, we assess the expressive power of CLTLoc, by comparing it with various temporal formalisms over dense time.When interpreted over timed words, CLTLoc is equivalent to Timed Automata. We also define a monadic theory of orders, extending the one introduced by Kamp, which is expressively equivalent to CLTLoc. We investigate a decidable extension with an arithmetical next operator, which allows the expression of timed non-ω-regular languages