On partial order semantics for SAT/SMT-based symbolic encodings of weak memory concurrency

TL;DR

This paper develops a theoretical foundation for partial order semantics in SAT/SMT-based symbolic encodings of weak memory concurrency, leading to more efficient bounded model checking.

Contribution

It introduces a decision procedure for a fragment of concurrent programs with fixed point operators and establishes an equivalence that reduces encoding size.

Findings

A decision procedure for a fragment with fixed point operators.

Equivalence between relaxed sequential consistency semantics and weak memory axioms.

Quadratic-size symbolic encoding for bounded model checking.

Abstract

Concurrent systems are notoriously difficult to analyze, and technological advances such as weak memory architectures greatly compound this problem. This has renewed interest in partial order semantics as a theoretical foundation for formal verification techniques. Among these, symbolic techniques have been shown to be particularly effective at finding concurrency-related bugs because they can leverage highly optimized decision procedures such as SAT/SMT solvers. This paper gives new fundamental results on partial order semantics for SAT/SMT-based symbolic encodings of weak memory concurrency. In particular, we give the theoretical basis for a decision procedure that can handle a fragment of concurrent programs endowed with least fixed point operators. In addition, we show that a certain partial order semantics of relaxed sequential consistency is equivalent to the conjunction of three extensively studied weak memory axioms by Alglave et al. An important consequence of this equivalence is an asymptotically smaller symbolic encoding for bounded model checking which has only a quadratic number of partial order constraints compared to the state-of-the-art cubic-size encoding.