What’s Decidable about Weak Memory Models?

Abstract

We investigate the decidability of the state reachability problem in finite-state programs running under weak memory models. In [3], we have shown that this problem is decidable for TSO and its extension with the write-to-write order relaxation, but beyond these models nothing is known to be decidable. Moreover, we have shown that relaxing the program order by allowing reads or writes to overtake reads leads to undecidability. In this paper, we refine these results by sharpening the (un)decidability frontiers on both sides. On the positive side, we introduce a new memory model NSW (for non-speculative writes) that extends TSO with the write-to-write relaxation, the read-to-read relaxation, and support for partial fences. We present a backtrack-free operational model for NSW, and prove that it does not allow causal cycles (thus barring pathological out-of-thin-air effects). On the negative side, we show that adding the read-to-write relaxation to TSO causes undecidability, and that adding non-atomic writes to NSW also causes undecidability. Our results establish that NSW is the first known hardware-centric memory model that is relaxed enough to permit both delayed execution of writes and early execution of reads for which the reachability problem is decidable.