Reachability and Safety Games under TSO Semantics (Extended Version)
Stephan Spengler
TL;DR
This work studies two-player games on concurrent programs running under the weak memory model $TSO$, with one player controlling program execution and the other controlling buffer updates. It shows that reachability and safety objectives in this setting reduce to single-process games, yielding a finite-state bisimulation and PSPACE-completeness in the absence of fairness. Introducing fairness constraints (update-fairness for writes and process-fairness for active processes) renders both reachability and safety undecidable, via reductions from perfect channel systems. The paper also analyzes load-buffer semantics as an alternative to store-buffer semantics and demonstrates that the equivalence in reachability does not extend to game-winning strategies. Overall, the results clarify the computational boundaries of reachability and safety under TSO and highlight how fairness and semantic choices impact decidability and strategies.
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.