Efficient May Happen in Parallel Analysis for Async-Finish Parallelism

For concurrent and parallel languages, the may-happen-in-parallel (MHP) decision problem asks, given two actions in the program, if there is an execution in which they can execute in parallel. Closely related, the MHP computation problem asks, given a program, which pairs of statements may happen in parallel. MHP analysis is the basis for many program analysis problems, such as data race detection and determinism checking, and researchers have devised MHP analyses for a variety of programming models. We present algorithms for static MHP analysis of a storeless abstraction of X10-like languages that have async-finish parallelism and procedures. For a program of size n, our first algorithm solves the MHP decision problem in O(n) time, via a reduction to constrained dynamic pushdown networks (CDPNs). Our second algorithm solves the MHP computation problem in O(n · max (n, k)) time, where k is a statically determined upper bound on the number of pairs that may happen in parallel. The second algorithm first runs a type-based analysis that produces a set of candidate pairs, and then it runs the decision procedure on each of those pairs. For programs without recursion, the type-based analysis is exact and gives an output-sensitive algorithm for the MHP computation problem, while for recursive programs, the type-based analysis may produce spurious pairs that the decision procedure will then remove. Our experiments on a large suite of X10 benchmarks suggest that our approach scales well. Our experiments also show that while k is O(n2) in the worst case, k is often O(n) in practice.