Reachability and Safety Games under TSO Semantics (Extended Version)

TL;DR

This paper studies reachability and safety games on concurrent programs under TSO semantics, showing their reduction to finite-state analysis and exploring the impact of fairness assumptions on decidability.

Contribution

It introduces a novel game-theoretic framework for TSO semantics and analyzes the decidability of reachability and safety problems under various fairness conditions.

Findings

Reachability and safety problems reduce to finite-state analysis.

Fairness assumptions lead to undecidability of these problems.

The framework models realistic concurrent behaviors under TSO.

Abstract

We consider games played on the transtion graph of concurrent programs running under the Total Store Order (TSO) weak memory model. Games are frequently used to model the interaction between a system and its environment, in this case between the concurrent processes and the nondeterminisitic TSO buffer updates. The game is played by two players, who alternatingly make a move: The process player can execute any enabled instruction of the processes, while the update player takes care of updating the messages in the buffers that are between each process andthe shared memory. We show that the reachability and safety problem of this game reduce to the analysis of single-process (non-concurrent) programs. In particular, they exhibit only finite-state behaviour. Because of this, we introduce different notions of fairness, which force the two players to behave in a more realistic way. Both the reachability and safety problem then become undecidable.