9 research outputs found
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
On the expressiveness and monitoring of metric temporal logic
It is known that Metric Temporal Logic (MTL) is strictly less expressive than the Monadic First-Order Logic of Order and Metric (FO[<, +1]) when interpreted over timed words; this remains true even when the time domain is bounded a priori. In this work, we present an extension of MTL with the same expressive power as FO[<, +1] over bounded timed words (and also, trivially, over time-bounded signals). We then show that expressive completeness also holds in the general (time-unbounded) case if we allow the use of rational constants q ∈ Q in formulas. This extended version of MTL therefore yields a definitive real-time analogue of Kamp’s theorem. As an application, we propose a trace-length independent monitoring procedure for our extension of MTL, the first such procedure in a dense real-time setting
On regions and zones for event-clock automata
Event clock automata (ECA) are a model for timed languages that has been introduced by Alur, Fix and Henzinger as an alternative to timed automata, with better theoretical properties (for instance, ECA are determinizable while timed automata are not). In this paper, we revisit and extend the theory of ECA. We first prove that no finite time abstract language equivalence exists for ECA, thereby disproving a claim in the original work on ECA. This means in particular that regions do not form a time abstract bisimulation. Nevertheless, we show that regions can still be used to build a finite automaton recognizing the untimed language of an ECA. Then, we extend the classical notions of zones and DBMs to let them handle event clocks instead of plain clocks (as in timed automata) by introducing event zones and Event DBMs (EDBMs). We discuss algorithms to handle event zones represented as EDBMs, as well as (semi-) algorithms based on EDBMs to decide language emptiness of ECA.Accepted for publicationSCOPUS: ar.jinfo:eu-repo/semantics/publishe
On Timed Automata with Input-Determined Guards
We consider a general notion of timed automata with inputdetermined guards and show that they admit a robust logical framework along the lines of [6], in terms of a monadic second order logic characterisation and an expressively complete timed temporal logic. We then generalize these automata using the notion of recursive operators introduced by Henzinger, Raskin, and Schobbens [10], and show that they admit a similar logical framework. These results hold in the pointwise semantics. We finally use this framework to show that the real-time logic MITL of Alur et al [2] is expressively complete with respect to an MSO corresponding to an appropriate set of input-determined operators