Backward coverability with pruning for lossy channel systems

Abstract

Driven by the concurrency revolution, the study of the coverability problem for Petri nets has regained a lot of interest in the recent years. A promising approach, which was presented in two papers last year, leverages a downward-closed forward invariant to accelerate the classical backward coverability analysis for Petri nets. In this paper, we propose a generalization of this approach to the class of well-structured transition systems (WSTSs), which contains Petri nets. We then apply this generalized approach to lossy channel systems (LCSs), a well-known subclass of WSTSs. We propose three downward-closed forward invariants for LCSs. One of them counts the number of messages in each channel, and the other two keep track of the order of messages. An experimental evaluation demonstrates the benefits of our approach.

The Ideal Approach to Computing Closed Subsets in Well-Quasi-orderings

“…This exponential blow-up essentially occurs when one has to distribute the unions over the products in order to retrieve an actual filter/ideal decomposition. We are not sure this can be averted, but when one only needs to represent certain particular closed subsets of (X * , ≤ * ), better representations do exist: see for instance [23].…”