On the Decidability of Verification under Release/Acquire

2026-04-15

AI Summary

This study addresses the decidability of reachability verification for concurrent programs under Release/Acquire weak memory models without atomic read-modify-write (RMW) operations. By employing formal modeling and reduction techniques, it establishes—for the first time—that the reachability problem remains undecidable even in the complete absence of RMW operations, thereby demonstrating that basic synchronization primitives alone suffice to induce undecidability in this model. Furthermore, the paper precisely characterizes the decidability boundary when both the number of context switches and the number of RMW operations are bounded, identifying sufficient conditions under which decidability is restored. These results provide a foundational theoretical basis for program verification under weak memory semantics.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

The verification of concurrent programs under weak-memory models is a burgeoning effort, owing to the increasing adoption of weak memory in concurrent software and hardware. Release/Acquire has become the standard model for high-performance concurrent programming, adopted by common mainstream languages and computer architectures. In a surprising result, Abdulla et al. (PLDI'19) proved that reachability in this model is undecidable when programs have access to atomic Read-Modify-Write (RMW) operations. Moreover, undecidability holds even for executions with just 4 contexts, and is thus immune to underapproximations based on bounded context switching. The canonical, RMW-free case was left as a challenging question, proving a non-primitive recursive lower bound as a first step, and has remained open for the past seven years. In this paper, we settle the above open question by proving that reachability is undecidable even in the RMW-free fragment of Release/Acquire, thereby characterizing the simplest set of communication primitives that gives rise to undecidability. Moreover, we prove that bounding both the number of context switches and the number of RMWs recovers decidability, thus fully characterizing the boundary of decidability along the dimensions of RMW-bounding and context-bounding.

Problem

• Release/Acquire
• reachability
• undecidability
• concurrent programs
• weak-memory models

Innovation

• Release/Acquire
• undecidability
• concurrent program verification
• weak memory model
• context-bounding