From Timed Automata to Logic - and Back

One of the most successful techniques for automatic verification is that of model checking. For finite automata there exist since long extremely efficient model–checking algorithms, and in the last few years these algorithms have been made applicable to the verification of real–time automata using the region–techniques of Alur and Dill. In this paper, we continue this transfer of existing techniques from the setting of finite (untimed) automata to that of timed automata. In particular, a timed logic Lν is put forward, which is sufficiently expressive that we for any timed automaton may construct a single characteristic Lν formula uniquely characterizing the automaton up to timed bisimilarity. Also, we prove decidability of the satisfiability problem for Lν with respect to given bounds on the number of clocks and constants of the timed automata to be constructed. None of these results have as yet been succesfully accounted for in the presence of time 1. ∗This work has been supported by the European Communities under CONCUR2, BRA 7166 †Basic Research in Computer Science, Centre of the Danish National Research Foundation. 1An exception occurs in Alur’s thesis [Alu91] in which a decidability result is presented for a linear timed logic called MITL.