Structural Invariants for the Verification of Systems with Parameterized Architectures

We consider parameterized concurrent systems consisting of a finite but unknown number of components, obtained by replicating a given set of finite state automata. Components communicate by executing atomic interactions whose participants update their states simultaneously. We introduce an interaction logic to specify both the type of interactions (e.g.\ rendez-vous, broadcast) and the topology of the system (e.g.\ pipeline, ring). The logic can be easily embedded in monadic second order logic of finitely many successors, and is therefore decidable. Proving safety properties of such a parameterized system, like deadlock freedom or mutual exclusion, requires to infer an inductive invariant that contains all reachable states of all system instances, and no unsafe state. We present a method to automatically synthesize inductive invariants directly from the formula describing the interactions, without costly fixed point iterations. We experimentally prove that this invariant is strong enough to verify safety properties of a large number of systems including textbook examples (dining philosophers, synchronization schemes), classical mutual exclusion algorithms, cache-coherence protocols and self-stabilization algorithms, for an arbitrary number of components.Comment: preprint; to be published in the proceedings of TACAS2

Structural Invariants for the Verification of Systems with Parameterized Architectures

We consider parameterized concurrent systems consisting of a finite but unknown number of components, obtained by replicating a given set of finite state automata. Components communicate by executing atomic interactions whose participants update their states simultaneously. We introduce an interaction logic to specify both the type of interactions (e.g. rendezvous , broadcast) and the topology of the system (e.g. pipeline, ring). The logic can be easily embedded in monadic second logic of κ ≥ 1 successors (WSκS), and is therefore decidable. Proving safety properties of such a parameterized system, like deadlock freedom or mutual exclusion, requires to infer an inductive invariant that contains all reachable states of all system instances, and no unsafe state. We present a method to automatically synthesize inductive invariants directly from the formula describing the interactions , without costly fixed point iterations. We experimentally prove that this invariant is strong enough to verify many textbook examples, such as dining philosophers, mutual exclusion protocols, and concurrent systems with preemption and priorities, for an arbitrary number of components

Lifted structural invariant analysis of Petri net product lines

Petri nets are commonly used to represent concurrent systems. However, they lack support for modelling and analysing system families, like variants of controllers, different variations of a process model, or the possible configurations of a flexible assembly line. To facilitate modelling potentially large collections of similar systems, in this paper, we enrich Petri nets with variability mechanisms based on product line engineering. Moreover, we present methods for the efficient analysis of the place and transition invariants in all defined versions of a Petri net. Efficiency is achieved by analysing the system family as a whole, instead of analysing each possible net variant separately. For this purpose, we lift the notion of incidence matrix to the product line level, and rely on constraint solving techniques. We present tool support and evaluate the benefits of our techniques on synthetic and realistic examples, achieving in some cases speed-ups of two orders of magnitude with respect to analysing each net variant separatelyThis work has been funded by the Spanish Ministry of Science (PID2021-122270OB-I00) and the R&D programme of Madrid (P2018/TCS-4314

Structural Invariants for the Verification of Systems with Parameterized Architectures

International audienceWe consider parameterized concurrent systems consisting of a finite but unknown number of components, obtained by replicating a given set of finite state automata. Components communicate by executing atomic interactions whose participants update their states simultaneously. We introduce an interaction logic to specify both the type of interactions (e.g. rendezvous , broadcast) and the topology of the system (e.g. pipeline, ring). The logic can be easily embedded in monadic second logic of κ ≥ 1 successors (WSκS), and is therefore decidable. Proving safety properties of such a parameterized system, like deadlock freedom or mutual exclusion, requires to infer an inductive invariant that contains all reachable states of all system instances, and no unsafe state. We present a method to automatically synthesize inductive invariants directly from the formula describing the interactions , without costly fixed point iterations. We experimentally prove that this invariant is strong enough to verify many textbook examples, such as dining philosophers, mutual exclusion protocols, and concurrent systems with preemption and priorities, for an arbitrary number of components