On characteristic formulae for Event-Recording Automata^∗

¹ Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université Bordeaux 1, 351 cours de la Libération, 33405 Talence Cedex, France.
nguena@labri.fr
² Laboratoire d’Informatique Fondamentale (LIF), Aix-Marseille Université, 39 avenue Joliot-Curie, 13453 Marseille Cedex 13, France.
pierre-alain.reynier@lif.univ-mrs.fr

Received: 28 September 2012
Accepted: 28 September 2012

Abstract

A standard bridge between automata theory and logic is provided by the notion of characteristic formula. This paper investigates this problem for the class of event-recording automata (ERA), a subclass of timed automata in which clocks are associated with actions and that enjoys very good closure properties. We first study the problem of expressing characteristic formulae for ERA in Event-Recording Logic (ERL ), a logic introduced by Sorea to express event-based timed specifications. We prove that the construction proposed by Sorea for ERA without invariants is incorrect. More generally, we prove that timed bisimilarity cannot in general be expressed in ERL for the class of ERA , and study under which conditions on ERA it can be. Then, we introduce the logic WT_μ , a new logic for event-based timed specifications closer to the timed logic ℒ_ν that was introduced by Laroussinie, Larsen and Weise. We prove that it is strictly more expressive than ERL , and that its model-checking problem against ERA is EXPTIME -complete. Finally, we provide characteristic formulae constructions in WT_μ for characterizing the general class of ERA up to timed (bi)similarity and study the complexity issues.