Parameterized model checking of rendezvous systems

Abstract

Parameterized model checking is the problem of deciding if a given formula holds irrespective of the number of participating processes. A standard approach for solving the parameterized model checking problem is to reduce it to model checking finitely many finite-state systems. This work considers the theoretical power and limitations of this technique. We focus on concurrent systems in which processes communicate via pairwise rendezvous, as well as the special cases of disjunctive guards and token passing; specifications are expressed in indexed temporal logic without the next operator; and the underlying network topologies are generated by suitable formulas and graph operations. First, we settle the exact computational complexity of the parameterized model checking problem for some of our concurrent systems, and establish new decidability results for others. Second, we consider the cases where model checking the parameterized system can be reduced to model checking some fixed number of processes, the number is known as a cutoff. We provide many cases for when such cutoffs can be computed, establish lower bounds on the size of such cutoffs, and identify cases where no cutoff exists. Third, we consider cases for which the parameterized system is equivalent to a single finite-state system (more precisely a Büchi word automaton), and establish tight bounds on the sizes of such automata.

Architecture Modelling of Parametric Component-Based Systems

“…Our logic is proved sufficient to model several complex architectures. This is important because parametric systems based on well-defined architectures satisfy most of their requirements [4,9].…”

“…We present a FOEIL sentence ψ for Request/Response architecture, described in Example 2, in the parametric setting. Let X (1) , X (2) , X (3) , and X (4) refer to instances of service registry, service, client, and coordinator component, respectively. Then, ψ = ∃x (1) .…”

“…Parametric systems represent a wide class of component-based systems including communication protocols and concurrent and distributed algorithms [1,9,17]. Parametric systems are constructed by a finite number of component types each consisting of an unknown number of instances [4,9]. We address the problem of modelling the ordering restrictions for the components' connections, an important aspect of several parametric architectures, including Publish/Subscribe and Request/Response [15,38].…”

“…Specifically, we consider the architectures Blackboard, Request/Response, and Publish/Subscribe, that impose orders on the implementation of their interactions. (4) We state an effective translation of FOEIL formulas to finite automata and prove the decidability of equivalence, validity and satisfiability for FOEIL sentences.…”

Promptness and Bounded Fairness in Concurrent and Parameterized Systems

“…The types of systems for which we prove these results include guarded protocols, as introduced by Emerson and Kahlon [14], and token-passing systems, as introduced by Emerson and Namjoshi [13] for uni-directional rings, and by Clarke et al [10] for arbitrary topologies. Parameterized model checking for both of these system classes has recently been further investigated [2,3,5,22,30,31], but thus far not in a context that includes promptness properties.…”