Complete Local Reasoning About Parameterized Programs Over Topologies

2026-05-14

AI Summary

This work addresses the problem of safety verification for infinite-state parameterized concurrent programs under various communication topologies. To this end, it proposes a topology-aware compositional verification method that, for the first time, completely reduces parameterized program verification to local reasoning under mild topological assumptions. The approach further enables the automatic synthesis of universally quantified inductive invariants. A prototype implementation demonstrates the practicality and scalability of the method by successfully verifying safety properties across a range of benchmark programs featuring representative communication topologies.

Abstract

This paper investigates the algorithmic safety verification problem of infinite-state parameterized concurrent programs over a rich set of communication topologies. The goal is to automatically produce a proof of correctness in the form of a universally quantified inductive invariant, where the quantification is over the nodes in the topology. We illustrate that under reasonable assumptions on the underlying topology, the problem can be reduced to and solved as a compositional scheme, that is, the verification of the parameterized family is reduced to a set of local proofs, in a complete manner. We propose a verification algorithm, which is implemented as a tool, and demonstrate through a set of benchmarks over several different topologies that our approach is effective in proving parameterized programs safe.

Problem

• parameterized programs
• safety verification
• inductive invariant
• communication topologies
• concurrent programs

Innovation

• parameterized verification
• local reasoning
• compositional verification
• inductive invariant
• topology-aware concurrency