From timed automata to logic — and back

Abstract

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 L ν is put forward, which is sufficiently expressive that we for any timed automaton may construct a single characteristic L ν formula uniquely characterizing the automaton up to timed bisimilarity. Also, we prove decidability of the satisfiability problem for L ν 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. 1 An exception occurs in Alur's thesis [Alu91] in which a decidability result is presented for a linear timed logic called MITL.

Binary Reachability Analysis of Pushdown Timed Automata with Dense Clocks

“…In particular, by using the standard region technique, it has been shown that region reachability for timed automata is decidable [3]. This fundamental result and the technique help researchers, both theoretically and practically, in formulating various timed temporal logics [2,4,5,6,22,25,26,27] and developing verification tools [21,28,24].…”

A Unifying Approach to Decide Relations for Timed Automata and their Game Characterization

“…A characteristic formula is a significantly complex formula describing the entire behaviour of the timed automaton. Here we describe how we can in general generate a simpler formula using a fragment of the logic described in [14]. The logic we use for generating the distinguishing formula has been described in [1] which is a timed extension of Hennessy-Milner logic and does not contain any recursion as opposed to the logic used in [14].…”

“…Here we describe how we can in general generate a simpler formula using a fragment of the logic described in [14]. The logic we use for generating the distinguishing formula has been described in [1] which is a timed extension of Hennessy-Milner logic and does not contain any recursion as opposed to the logic used in [14]. The set M t of Hennessy-Milner logic formulae with time over a set of actions Act, set D of formula clocks (distinct from the clocks of any timed automaton) is generated by the abstract syntax…”

“…The decidability of timed bisimilarity between two timed automata was proved in [4] via a product construction on region graphs. [14] also uses regions as the basis of checking timed bisimilarity for timed automata. To overcome the state space explosion in region graphs, [22] applies the product construction on zone graphs.…”

“…Moreover, the product based approach cannot be used to check all possible relations, for instance, it is not useful in checking timed performance prebisimulation [11]. Corresponding to each of the bisimulation relations described above, we can consider a simulation relation and our zone graph can be used to check all these relations in a uniform way, Further, our method checks timed bisimulation between two states with arbitrary rational valuations; many of the existing approaches [14], can only check for timed bisimulation between the initial states.…”