Detecting Race Conditions in Parallel Programs that Use Semaphores

TL;DR

This paper investigates the computational complexity of detecting race conditions in semaphore-based parallel programs, proving NP-completeness for two semaphores and providing efficient algorithms for the single semaphore case.

Contribution

It establishes NP-completeness for race detection with two semaphores and introduces two efficient algorithms for race detection when only one semaphore is used.

Findings

NP-complete to detect race conditions with two semaphores

O(n) algorithm for race detection between two operations

O(np log n) algorithm providing a compact race detection representation

Abstract

We address the problem of detecting race conditions in programs that use semaphores for synchronization. Netzer and Miller showed that it is NP-complete to detect race conditions in programs that use many semaphores. We show in this paper that it remains NP-complete even if only two semaphores are used in the parallel programs. For the tractable case, i.e., using only one semaphore, we give two algorithms for detecting race conditions from the trace of executing a parallel program on p processors, where n semaphore operations are executed. The first algorithm determines in O(n) time whether a race condition exists between any two given operations. The second algorithm runs in O(np log n) time and outputs a compact representation from which one can determine in O(1) time whether a race condition exists between any two given operations. The second algorithm is near-optimal in that the running time is only O(log n) times the time required simply to write down the output.