Parameterized Model Checking of Rendezvous Systems

Abstract

We study the complexity of the model-checking problem for parameterized discrete-timed systems with arbitrarily many anonymous and identical contributors, with and without a distinguished "controller" process. Processes communicate via synchronous rendezvous. Our work extends the seminal work on untimed systems [German, Sistla: Reasoning about Systems with Many Processes. J. ACM 39(3), 1992] by the addition of discrete-time clocks, thus allowing one to model more realistic protocols.For the case without a controller, we show that the systems can be efficiently simulated -and vice versa -by systems of untimed processes that communicate via rendezvous and symmetric broadcast, which we call "RB-systems". Symmetric broadcast is a novel communication primitive that, like ordinary asymmetric broadcast allows all processes to synchronize; however, it has no distinction between sender/receiver processes.We show that the complexity of the parameterized model-checking problem for safety specifications is pspace-complete, and for liveness specifications it is decidable and in exptime. The latter result is proved using automata theory, rational linear programming, and geometric reasoning for solving certain reachability questions in a new variant of vector addition systems called "vector rendezvous systems". We believe these proof techniques are of independent interest and will be useful in solving related problems.For the case with a controller, we show that the parameterized model-checking problems for RB-systems and systems with asymmetric broadcast as a primitive are inter-reducible. This allows us to prove that for discrete timed-networks with a controller the parameterized model-checking problem is undecidable for liveness specifications.Our work exploits the intimate and fruitful connection between parameterized discretetimed systems and systems of processes communicating via broadcast. This allows us to provide a rare and surprising decidability result for liveness properties of parameterized timed-systems, as well as extend work from untimed systems to timed systems.

Parameterized model checking of rendezvous systems

“…(iii) The sets of topologies we consider all have either bounded tree-width, or more generally bounded cliquewidth, and are expressible in one of three ways. 3 1. Using MSO, a powerful and general formalism for describing sets of topologies, which can express e.g., planarity, acyclicity and -connectivity.…”

“…The disjunction in the last formula is over all elements C of Char Remark 2 (Fairness) The conference version of this paper [3] assumed that token-passing systems satisfy a fairness condition, namely that the token visits every process infinitely often. In contrast, the presentation in this paper does not require this fairness condition to hold.…”

“…In contrast, the presentation in this paper does not require this fairness condition to hold. Elimination of the fairness condition is the reason that we replaced the treatment of ≡ CTL * d \X equivalence classes using contractions based on [2] in [3] with a treatment using CTL…”

Discrete Parameters in Petri Nets

“…Informally, the idea is that the reachability of bad configurations can be detected with only a small number of processes. In [Aminof et al, 2014] a similar analysis technique is notably addressed on concurrent systems in which processes communicate via pairwise rendezvous.…”

Verification of Asynchronous Mobile-Robots in Partially-Known Environments

“…By simplifying the systems (e.g., restricting the mode of communication, the abilities of the processes, the specification languages, etc.) one can get decidable parameterised verification, recently e.g., [12,[1][2][3].…”