Occurrence Counting Analysis for the π-calculus

Abstract

We propose an abstract interpretation-based analysis for automatically proving non-trivial properties of mobile systems of processes. We focus on properties relying on the number of occurrences of processes during computation sequences, such as mutual exclusion and non-exhaustion of resources.We design a non-standard semantics for the π-calculus in order to explicitly trace the origin of channels and to solve efficiently problems set by α-conversion and non-deterministic choices. We abstract this semantics into an approximate one. The use of a relational domain for counting the occurrences of processes allows us to prove quickly and efficiently properties such as mutual exclusion and non-exhaustion of resources. At last, dynamic partitioning allows us to detect some configurations by which no infinite computation sequences can pass.