Multi-execution memory models, such as Promising and Weakestmo, are an advanced class of weak memory
consistency models that justify certain outcomes of a concurrent program by considering multiple candidate executions collectively. While this key characteristic allows them to support effective compilation to hardware models and a wide range of compiler optimizations, it makes reasoning about them substantially more difficult. In particular, we observe that Promising and Weakestmo inhibit effective model checking because they allow some suprisingly weak behaviors that cannot be generated by examining one execution at a time.

We therefore introduce Weakestmo2, a strengthening of Weakestmo by constraining its multi-execution
nature, while preserving the important properties of Weakestmo: DRF theorems, compilation to hardware models, and correctness of local program transformations. Our strengthening rules out a class of surprisingly weak program behaviors, which we attempt to characterize with the help of two novel properties: load buffering race freedom and certification locality. In addition, we develop WMC, a model checker for Weakestmo2 with performance close to that of the best tools for per-execution models.