Learning to prove safety over parameterised concurrent systems

Abstract

Learning to prove safety over parameterised concurrent systems. In: Proc. 17th International Conference on Formal Methods in Computer-AidedDesign (pp. 76-83 Abstract-We revisit the classic problem of proving safety over parameterised concurrent systems, i.e., an infinite family of finite-state concurrent systems that are represented by some finite (symbolic) means. An example of such an infinite family is a dining philosopher protocol with any number n of processes (n being the parameter that defines the infinite family). Regular model checking is a well-known generic framework for modelling parameterised concurrent systems, where an infinite set of configurations (resp. transitions) is represented by a regular set (resp. regular transducer). Although verifying safety properties in the regular model checking framework is undecidable in general, many sophisticated semi-algorithms have been developed in the past fifteen years that can successfully prove safety in many practical instances. In this paper, we propose a simple solution to synthesise regular inductive invariants that makes use of Angluin's classic L * algorithm (and its variants). We provide a termination guarantee when the set of configurations reachable from a given set of initial configurations is regular. We have tested L * algorithm on standard (as well as new) examples in regular model checking including the dining philosopher protocol, the dining cryptographer protocol, and several mutual exclusion protocols (e.g. Bakery, Burns, Szymanski, and German). Our experiments show that, despite the simplicity of our solution, it can perform at least as well as existing semi-algorithms.

Structural Invariants for the Verification of Systems with Parameterized Architectures

“…An exhaustive chart of decidability results for verification of parameterized systems is drawn in [12]. When decidability is not of concern, over-approximating and semi-algorithmic techniques such as regular model checking [33,2], SMT-based bounded model checking [4,19], abstraction [10,14] and automata learning [17] can be used to deal with more general classes of systems.…”

“…An exhaustive chart of decidability results for verification of parameterized systems is drawn in [12]. When decidability is not of concern, over-approximating and semi-algorithmic techniques such as regular model checking [33,2], SMT-based bounded model checking [4,19], abstraction [10,14] and automata learning [17] can be used to deal with more general classes of systems.The efficiency of a verification method crucially relies on its ability to synthesize an inductive safety invariant, i.e., an infinite set of configurations that contains the initial configurations, is closed under the transition relation, and excludes the error configurations. In general, automatically synthesizing invariants requires computationally expensive fixpoint iterations [20].…”

“…Herman: This algorithm implements self-stabilizing token passing in rings. The formulation as well as all following follow [17]. Israeli-Jalfon: This is another self-stabilizing token passing algorithm in rings.…”

Probabilistic Bisimulation for Parameterized Systems

“…We propose an automata learning method to automatically compute regular probabilistic bisimulations R, focusing on the case of length-preserving PTSs, which covers all examples given in the previous section. The approach uses active automata learning, for instance Angluin's L * method [5] or refinements of it, to compute R. This approach is inspired by previous work on using active automata learning for invariant inference [18,54]. Our procedure assumes (i) as input a bounded-branching PTS S = S; {δ a } a∈ACT , as well as a length-preserving regular relation E ⊆ (Σ × Σ) * supposed to be covered by R; (ii) an effective way to check the correctness of R, i.e., a decision procedure in the sense of Theorem 1; and (iii) a procedure to compute the greatest probabilistic bisimulationR n ⊆ (Σ × Σ) n for S restricted to configurations of any length n ∈ N. The last assumption can easily be satisfied for length-preserving PTSs.…”

Checking Deadlock-Freedom of Parametric Component-Based Systems

“…Typically, these methods apply to systems with global coordination. When theoretical decidability is not of concern, semi-algorithmic techniques such as regular model checking [16,2], SMT-based bounded model checking [3,13], abstraction [7,10] and automata learning [12] can be used to deal with more Institute of Engineering Univ. Grenoble Alpes general classes of The interested reader can find a complete survey on parameterized model checking by Bloem et al [9].…”