Determinacy and Repeatability of Parallel Program Schemata

The concept of "determinism" of parallel programs and parallel systems has received a lot of attention since the dawn of computing, with multiple proposals for formal and informal definitions of deterministic execution. In this paper, we present precise definitions of two related properties of program schemata - determinacy and repeatability. A key advantage of providing definitions for schemata rather than concrete programs is that it simplifies the task for programmers and tools to check these properties. The definitions of these properties are provided for schemata arising from data flow programs and task-parallel programs, thereby also establishing new relationships between the two models. Our hope is that these definitions will help provide a framework for enabling more precise definitions of determinism in future work.