Parameterized Verification of Asynchronous Round-Based Distributed Algorithms via Reduction to Finite-Counter Systems

2026-06-26

AI Summary

This work addresses the challenge of parameterized verification for asynchronous round-based distributed algorithms, which is complicated by the infinite-state nature of individual processes. While the problem is shown to be undecidable, this paper presents the first reduction to LTL model checking over finite counter systems, enabling complete verification of safety and liveness properties for arbitrarily many processes. By integrating this reduction with LTL model checking and the symbolic model checker nuXmv, the approach successfully verifies several asynchronous round-based consensus and leader election algorithms, demonstrating both feasibility and effectiveness.

Abstract

Traditional model-checking techniques typically verify distributed algorithms only for a fixed number of finite-state processes. Parameterized model checking generalizes this to any number of processes, while still typically assuming that each process is finite-state. In this work, we consider asynchronous round-based distributed algorithms in which each process is infinite-state since it can execute for an infinite number of rounds. We show that the parameterized verification problem for asynchronous round-based distributed algorithms is undecidable, already for simple specifications. Nevertheless, as our main contribution, we provide a reduction to LTL model checking over finite-counter systems and prove that it is sound and complete. This enables the use of off-the-shelf, mature symbolic model checkers for finite-counter systems. We demonstrate the practical applicability of this reduction by verifying safety and liveness properties of several asynchronous round-based consensus and leader-election algorithms using the nuXmv model checker.

Problem

• parameterized verification
• asynchronous round-based distributed algorithms
• infinite-state processes
• undecidability
• distributed consensus

Innovation

• parameterized verification
• asynchronous round-based algorithms
• finite-counter systems
• LTL model checking
• undecidability