Parameterized Model-Checking of Timed Systems with Conjunctive Guards

Abstract

In this work we extend the Emerson and Kahlon's cutoff theorems for process skeletons with conjunctive guards to Parameterized Networks of Timed Automata, i.e. systems obtained by an apriori unknown number of Timed Automata instantiated from a finite set U1, . . . , Un of Timed Automata templates. In this way we aim at giving a tool to universally verify software systems where an unknown number of software components (i.e. processes) interact with continuous time temporal constraints. It is often the case, indeed, that distributed algorithms show an heterogeneous nature, combining dynamic aspects with real-time aspects. In the paper we will also show how to model check a protocol that uses special variables storing identifiers of the participating processes (i.e. PIDs) in Timed Automata with conjunctive guards. This is non-trivial, since solutions to the parameterized verification problem often relies on the processes to be symmetric, i.e. indistinguishable. On the other side, many popular distributed algorithms make use of PIDs and thus cannot directly apply those solutions. arXiv:1407.7305v2 [cs.LO]

Accuracy of Message Counting Abstraction in Fault-Tolerant Distributed Algorithms

“…Most of the results about PMC of timed systems [2,31,8,10,3,1,34,9] are restricted to systems whose interprocess communication primitives have other systems in mind than FTDAs. For instance, the local state space is fixed and finite and independent of the parameters, while message counting in FTDAs requires that the local state space depends on the parameters.…”

“…This motivated us to introduce the notions of message passing timed automata and message counting timed automata. Besides, the literature typically focuses on decidability, e.g., [3,1,34,9] analyze decidability for different variants of the parameterized model checking problem (e.g., integer vs. continuous time, safety vs. liveness, presence vs. absence of controller). Our work focuses on establishing relations between different timed models, with the goal of using these relations for abstraction-based model checking.…”

Parameterized model checking of rendezvous systems

“…Although the PMCP is undecidable in general (see [28,52]) it becomes decidable for some combinations of communication primitives, network topologies, and specification languages, e.g., [1,8,14,21,22,30,51]. Often, it is proved decidable by a reduction to model checking finitely many finite-state systems [2,16,24,28,36].…”

Liveness of Parameterized Timed Networks

“…We consider the parameterized model-checking problem (PMCP) for timed networks: Does a given specification (usually given by a suitable automaton) hold for every system size? Apart from a single result which deals with much weaker synchronization than rendezvous [13], no positive PMCP results for liveness specifications of timed automata are known.…”

“…The main difference between our work and theirs is: we do not have a controller, we make no additional restrictions, and we can model check specifications given by B-or S-automata. The authors in [13] proved that the PMCP is decidable for continuous timed networks synchronizing using conjunctive Boolean guards and MITL and TCTL specifications. Finally, there are many decidability and undecidability results in the untimed setting, e.g., [14,9,8,4,5].…”