On the Power of Cliques in the Parameterized Verification of Ad Hoc Networks

Abstract

We study decision problems for parameterized verification of protocols for ad hoc networks. The problem we consider is control state reachability for networks of arbitrary size. We restrict our analysis to topologies that approximate the notion of bounded diameter often used in ad hoc networks for optimizing broadcast communication. We show that restricting to graphs with bounded diameter is not sufficient to make control state reachability decidable, but the problem turns out to be decidable when considering an additionally restricted class of graphs that still includes cliques. Although decidable, the problem is already Ackermann-hard over clique graphs.

On the Verification of Timed Ad Hoc Networks

“…We also mention decidability for DTAHN on cliques since, as for bounded paths, it derives from an application of the theory of wsts. Undecidability for DTAHN on graphs with bounded diameter follows instead from the result obtained in the untimed case in [6].…”

“…[8,12,11,5,6]. Ad hoc networks consist of wireless hosts that, in absence of a fixed infrastructure, communicate sending broadcast messages.…”

“…Following [5,6], in this paper we study decidability and undecidability properties of the local state reachability problem parametric on the initial configuration of a TAHN, i.e., the problem of checking the existence of an initial configuration that can evolve using continuous and discrete steps into a configuration exposing a given local state -usually representing an error.…”

“…The same holds for cliques of arbitrary order as in the case of dense time. Related Work Decidability issues for untimed models of ad hoc Networks have been considered in [5,6]. Model checking for timed automata has been applied to verify protocols for ad hoc networks with a fixed number of nodes in [8].…”

Parameterized Verification of Communicating Automata under Context Bounds

“…Lately, there has been a lot of (ongoing) research in the area of parameterized verification [1,3,9,13,14], which aims to validate a given system independently of the number of processes and the communication topology. A lot of different models of such systems have been proposed (cf.…”