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arXiv · 2502.15391

Counting Abstraction for the Verification of Structured Parameterized Networks

Marius Bozga·Radu Iosif·Arnaud Sangnier·Neven Villani
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Abstract

We consider the verification of parameterized networks of replicated processes whose architecture is described by hyperedge-replacement graph grammars. Due to the undecidability of verification problems such as reachability or coverability of a given configuration, in which we count the number of replicas in each local state, we develop two orthogonal verification techniques. We present a counting abstraction able to produce, from a graph grammar describing a parameterized system, a finite set of Petri nets that over-approximate the behaviors of the original system. The counting abstraction is implemented in a prototype tool, evalutated on a non-trivial set of test cases. Moreover, we identify a decidable fragment, for which the coverability problem is in 2EXPTIME and PSPACE-hard.

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Marius Bozga, Radu Iosif, Arnaud Sangnier, Neven Villani. 2025-02-21. Counting Abstraction for the Verification of Structured Parameterized Networks. https://arxiv.org/abs/2502.15391

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