Parameterized Verification of Communicating Automata under Context Bounds

Abstract

Abstract. We study the verification problem for parameterized communicating automata (PCA), in which processes synchronize via message passing. A given PCA can be run on any topology of bounded degree (such as pipelines, rings, or ranked trees), and communication may take place between any two processes that are adjacent in the topology. Parameterized verification asks if there is a topology from a given topology class that allows for an accepting run of the given PCA. In general, this problem is undecidable even for synchronous communication and simple pipeline topologies. We therefore consider context-bounded verification, which restricts the behavior of each single process. For several variants of context bounds, we show that parameterized verification over pipelines, rings, and ranked trees is decidable. More precisely, it is PSPACE-complete for pipelines and rings, and EXPTIME-complete for ranked trees. Our approach is automata-theoretic. We build a finite (tree, respectively) automaton that identifies those topologies that allow for an accepting run of the given PCA. The verification problem then reduces to checking nonemptiness of that automaton.

Verification of Parameterized Communicating Automata via Split-Width

“…Remark 23. We could also want to reason about a specific class T of topologies among the classes of pipelines, rings, or trees, as in [6,7]. This can be done with slight modifications of A k msc , resulting in an automaton that recognizes exactly the set of valid k-DSTs t such that T Mt ∈ T. There are many equivalent definitions of tree-width.…”

“…In particular, we consider existentially bounded or context bounded behaviors. But our approach based on split-width is generic since it can be easily adapted to other under-approximation classes, and it relaxes the assumptions of [6,7] which only considered rendez-vous syncronization and pipeline, ring, or tree topologies. In the case of context bounds, we show that it is sufficient to assume that the communication topology has bounded tree-width.…”

“…The emptiness and model-checking problems for PCAs have been considered in [6] and [7], respectively. Both papers assume rendez-vous synchronization, and a fixed class of topologies: pipelines, rings, or trees.…”

Deciding the existence of cut-off in parameterized rendez-vous networks

“…It is hence worth studying the complexity of the verification of such parameterized models and many recent works have attacked these problems considering networks with different means of communication. For instance in [16,13,7,6] the participants communicate thanks to broadcast of messages, in [11,2] they use a token-passing mechanism , in [10] a message passing mechanism and in [18] the communication is performed through shared registers. The relative expressiveness of some of those models has been studied in [4].…”

Adding Data Registers to Parameterized Networks with Broadcast

“…In [18], Esparza presents a survey of some of the main results for the above mentioned parameterized models. Parameterized verification of systems composed by repeated components have also been proposed by considering different means of communication as token-passing [5,9], message passing [7], or rendez-vous over an infinite domain of data in [11].…”