Bounded TSO-to-SC Linearizability Is Decidable

• Published in: SOFSEM 2016: Theory and Practice of Computer Science pp. 404 - 417
• Main Authors: Wang, Chao, Lv, Yi, Wu, Peng
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2016
• Series: Lecture Notes in Computer Science
• Subjects: Concurrent System; Memory Location; Memory Model; Operational Semantic; Return Action
• ISBN: 9783662491911; 3662491915
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-662-49192-8_33

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 $$\textit{cas}$$ 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.