Parameterized Verification of Asynchronous Shared-Memory Systems

TL;DR

This paper analyzes the computational complexity of safety verification in parameterized asynchronous shared-memory systems with different process models, revealing coNP-complete and PSPACE-complete results depending on the process type.

Contribution

It provides a detailed complexity characterization of safety verification for parameterized systems with leader and anonymous contributors across various computational models.

Findings

Verification is coNP-complete for finite-state processes.

Verification is PSPACE-complete for pushdown processes.

Bounded interactions with Turing machines keep the problem coNP-complete.

Abstract

We characterize the complexity of the safety verification problem for parameterized systems consisting of a leader process and arbitrarily many anonymous and identical contributors. Processes communicate through a shared, bounded-value register. While each operation on the register is atomic, there is no synchronization primitive to execute a sequence of operations atomically. We analyze the complexity of the safety verification problem when processes are modeled by finite-state machines, pushdown machines, and Turing machines. The problem is coNP-complete when all processes are finite-state machines, and is PSPACE-complete when they are pushdown machines. The complexity remains coNP-complete when each Turing machine is allowed boundedly many interactions with the register. Our proofs use combinatorial characterizations of computations in the model, and in case of pushdown-systems, some language-theoretic constructions of independent interest.