Bounded TSO-to-SC Linearizability Is Decidable - Wang, Chao; Lv, Yi; Wu, Peng (SOFSEM 2016: Theory and Practice of Computer Science, 2016)
TSO-to-SC linearizability is a variant of linearizability for concurrent libraries on the Total Store Order (TSO) memory model. In this paper we propose the notion of k-bounded TSO-to-SC linearizability, a subclass of TSO-to-SC linearizability that concerns only bounded histories. This subclass is non-trivial in that it does not restrict the number of write, flush and cas (compare-and-swap) actions, nor the size of a store buffer, to be bounded. We prove that the decision problem of k-bounded TSO-to-SC linearizability is decidable for a bounded number of processes. We first reduce this decision problem to a marked violation problem of k-bounded TSO-to-SC linearizability, where specific $$cas$$ actions are introduced to mark call and return actions. Then, we further reduce the marked violation problem to a control state reachability problem of a lossy channel machine, which is already known to be decidable. Moreover, we can show that the decision problem of k-bounded TSO-to-SC linearizability has non-primitive recursive complexity.