Logics vs. automata: The hybrid case

Abstract

We provided a framework for the specification and the verification of hybrid systems. We introduced a general specification logic HATL which is an extension of the temporal logic allowing constraints on bounded trajectories expressed by means of hybrid automata. We have shown how to translate verification problems stated in the automata-logic-based or in the logic-based approaches into the automata-based approach in order to apply algorithmic analysis techniques on automata. These translations are based on effective constructions of timed or hybrid automata from formulas in some fragments of HATL. Using these translations, we proved the decidability of the verification problems of timed Büchi automata w.r.t. TATL⁺ formulas, and of pure-time CDF formulas w.r.t. simple RF formulas.

The fragment TATL⁺ is a fairly powerful specification language since it subsumes deterministic timed Muller automata, and allows the expression of response as well as invariance timed properties. Its sublanguage TPTL⁺ constitues a fragment of TPTL whose verification problem is decidable. Moreover. TATL⁺ (as well as TPTL⁺) is not comparable with the known logics whose verification problem is decidable. as MITL and EMITL.

Pure-time CDF and simple RF are more expressive than the fragments of CoD that have been suggested to specify control systems and requirements. Thus, our results show, in particular, that the verification of CoD control designs w.r.t. CoD requirement formulas is decidable. This is the first decidability result concerning fragments of (dense time) CoD that are not purely propositional.

This work has been performed while this author was visiting Verimag.