#### The Reads-From Equivalence for the TSO and PSO Memory Models

##### Truc Lam Bui, Krishnendu Chatterjee, Tushar Gautam, Andreas Pavlogiannis, Viktor Toman

The verification of concurrent programs remains an open challenge due to the non-determinism in inter-process communication. Instead of exploring concrete executions, stateless model-checking (SMC) techniques partition the execution space into equivalence classes, and explore each class as opposed to each execution. For the relaxed memory models of TSO and PSO (total/partial store order), the standard equivalence has been Shasha-Snir traces, seen as an extension of the classic Mazurkiewicz equivalence from SC (sequential consistency) to TSO and PSO. The reads-from (RF) equivalence was recently shown to be coarser than the Mazurkiewicz equivalence, leading to impressive scalability improvements for SMC under SC. The generalization of RF to TSO and PSO requires to overcome two challenges, namely, verifying execution consistency and SMC algorithm. We address these two fundamental problems in this work. Our first set of contributions is on the problem of verifying TSO- and PSO-consistent executions given a reads-from map, VTSO-rf and VPSO-rf, respectively. The problem has been heavily studied under SC due to its numerous applications, but little is known for TSO and PSO. For an execution of $n$ events over $k$ threads and $d$ variables, we establish novel bounds that scale as $n^{k+1}$ for TSO and as $n^{k+1}\cdot \min(n^{k^2}, 2^{k\cdot d})$ for PSO. Our second contribution is an algorithm for SMC under TSO and PSO using the RF equivalence. Our algorithm is exploration-optimal, in the sense that it is guaranteed to explore each class of the RF partitioning exactly once, and spends polynomial time per class when $k$ is bounded. Our experimental evaluation shows that the RF equivalence is often exponentially coarser than Shasha-Snir traces, and our SMC algorithm scales much better than state-of-the-art tools based on Shasha-Snir traces.

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