Deciding the Satisfiability of MITL Specifications

In this paper we present a satisfiability-preserving reduction from MITL interpreted over finitely-variable continuous behaviors to Constraint LTL over clocks, a variant of CLTL that is decidable, and for which an SMT-based bounded satisfiability checker is available. The result is a new complete and effective decision procedure for MITL. Although decision procedures for MITL 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 MITL based on the encoding presented here has, instead, been implemented and is publicly available.Comment: In Proceedings GandALF 2013, arXiv:1307.416

Mightyl: A compositional translation from mitl to timed automata

Metric Interval Temporal Logic (MITL) was first proposed in the early 1990s as a specification formalism for real-time systems. Apart from its appealing intuitive syntax, there are also theoretical evidences that make MITL a prime real-time counterpart of Linear Temporal Logic (LTL). Unfortunately, the tool support for MITL verification is still lacking to this day. In this paper, we propose a new construction from MITL to timed automata via very-weak one-clock alternating timed automata. Our construction subsumes the well-known construction from LTL to Büchi automata by Gastin and Oddoux and yet has the additional benefits of being compositional and integrating easily with existing tools. We implement the construction in our new tool MightyL and report on experiments using Uppaal and LTSmin as back-ends

Satisfiability Checking for Mission-Time LTL

Mission-time LTL (MLTL) is a bounded variant of MTL over naturals designed to generically specify requirements for mission-based system operation common to aircraft, spacecraft, vehicles, and robots. Despite the utility of MLTL as a specification logic, major gaps remain in analyzing MLTL, e.g., for specification debugging or model checking, centering on the absence of any complete MLTL satisfiability checker. We prove that the MLTL satisfiability checking problem is NEXPTIME-complete and that satisfiability checking MLTL0 , the variant of MLTL where all intervals start at 0, is PSPACE-complete. We introduce translations for MLTL-to-LTL, MLTL-to-LTLf , MLTL-to-SMV, and MLTL-to-SMT, creating four options for MLTL satisfiability checking. Our extensive experimental evaluation shows that the MLTL-to-SMT transition with the Z3 SMT solver offers the most scalable performance

How bit-vector logic can help improve the verification of LTL specifications over infinite domains

Propositional Linear Temporal Logic (LTL) is well-suited for describing properties of timed systems in which data belong to finite domains. However, when one needs to capture infinite domains, as is typically the case in software systems, extensions of LTL are better suited to be used as specification languages. Constraint LTL (CLTL) and its variant CLTL-over-clocks (CLTLoc) are examples of such extensions; both logics are decidable, and so-called bounded decision procedures based on Satisfiability Modulo Theories (SMT) solving techniques have been implemented for them. In this paper we adapt a previously-introduced bounded decision procedure for LTL based on Bit-Vector Logic to deal with the infinite domains that are typical of CLTL and CLTLoc. We report on a thorough experimental comparison, which was carried out between the existing tool and the new, Bit-Vector Logic-based one, and we show how the latter outperforms the former in the vast majority of cases

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