Multi-clock timed networks

Abstract

Abstract. We consider verification of safety properties for parameterized systems of timed processes, so called timed networks. A timed network consists of a finite state process, called a controller, and an arbitrary set of identical timed processes. In a previous work, we showed that checking safety properties is decidable in the case where each timed process is equipped with a single real-valued clock. It was left open whether the result could be extended to multi-clock timed networks. We show that the problem becomes undecidable when each timed process has two clocks. On the other hand, we show that the problem is decidable when clocks range over a discrete time domain. This decidability result holds when processes have any finite number of clocks.

On the Verification of Timed Ad Hoc Networks

“…The task is to check whether q is reachable or not. In [2], the following result is shown. (2) is undecidable.…”

“…We observe however that protocols for ad hoc networks are often based on time-sensitive conditions like time-outs or time-stamps (added to flooded data). Parameterized verification of timed automata has been studied only for fully connected networks and rendez-vous communication (Timed Networks) in [4,2,3].…”

MCMT in the Land of Parametrized Timed Automata

“…This notion of parametrised timed network is first formalized in [4]. In the rest of this section, we recast such a notion into the formal framework of [13] underlying the infinite state model checker mcmt, which will be used to solve parametrised reachability problems of timed networks.…”

“…In the literature, there exist several variations and generalizations of the notion of parametrised timed networks introduced in [4] and formalized above in our framework. For example, delay transitions can be extended with location invariants, that can be used to force a process 'to react,' i.e.…”

“…Hence, there are two dimensions along which these systems are infinite state. Surprisingly, it is possible to show that the reachability problem for restricted classes of parametrised timed networks is decidable under suitable assumptions (e.g., on the number of clock variables or on the granularity of time) [4,5] by a backward reachability procedure. Despite these theoretical results, there are few systems capable of automatically solving parametrised and timed reachability problems.…”