On Characteristic Formulae for Event-Recording Automata

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 (complementation, determinization...). 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 false. More generally, we prove that bisimulation can not be expressed in ERL for the class of ERA, even without invariants. Then, we introduce the logic WTμ, a new logic for event-based timed specifications, closer to the timed logic Lν . We prove that it is strictly more expressive than ERL, and that its model-checking problem against ERA is EXPTIME-complete. Finally, we provide constructions for characterizing ERA up to timed (bi)similarity and study the complexity issues.