A Framework for Consistency Algorithms

TL;DR

This paper introduces a universal framework that generates deterministic algorithms for checking memory consistency in concurrent programs, achieving optimal performance for models like SC, TSO, PSO, and RMO.

Contribution

The authors develop a universal consistency problem framework that produces efficient algorithms for multiple memory models, demonstrating optimality under the exponential time hypothesis.

Findings

Algorithms for SC, TSO, and PSO are proven optimal under the exponential time hypothesis.

The framework produces algorithms with runtime O*(2^k) based on the number of write accesses.

The framework can be instantiated for various memory models, providing a unified approach.

Abstract

We present a framework that provides deterministic consistency algorithms for given memory models. Such an algorithm checks whether the executions of a shared-memory concurrent program are consistent under the axioms defined by a model. For memory models like SC and TSO, checking consistency is NP-complete. Our framework shows, that despite the hardness, fast deterministic consistency algorithms can be obtained by employing tools from fine-grained complexity. The framework is based on a universal consistency problem which can be instantiated by different memory models. We construct an algorithm for the problem running in time O*(2^k), where k is the number of write accesses in the execution that is checked for consistency. Each instance of the framework then admits an O*(2^k)-time consistency algorithm. By applying the framework, we obtain corresponding consistency algorithms for SC, TSO, PSO, and RMO. Moreover, we show that the obtained algorithms for SC, TSO, and PSO are optimal in the fine-grained sense: there is no consistency algorithm for these running in time 2^o(k) unless the exponential time hypothesis fails.