Correctness of Dynamic Dependence Analysis for Implicitly Parallel Tasking Systems

In this paper, we rigorously verify the correctness of dynamic dependence analysis, a key algorithm for parallelizing programs in implicitly parallel tasking systems. A dynamic dependence analysis of a program results in a task graph, a DAG of tasks constraining the order of task execution. Because a program is automatically parallelized based on its task graph, the analysis algorithm must generate a graph with all the dependencies that are necessary to preserve the program's original semantics for any non-deterministic parallel execution of tasks. However, this correctness is not straightforward to verify as implicitly parallel tasking systems often use an optimized dependence analysis algorithm. To study the correctness of dynamic dependence analysis in a realistic setting, we design a model algorithm that captures the essence of realistic analysis algorithms. We prove that this algorithm constructs task graphs that soundly and completely express correct parallel executions of programs. We also show that the generated task graph is the most succinct one for a program when the program satisfies certain conditions.