Parallel Algorithms for Predicate Detection

Given a trace of a distributed computation and a desired predicate, the predicate detection problem is to find a consistent global state that satisfies the given predicate. The predicate detection problem has many applications in the testing and runtime verification of parallel and distributed systems. We show that many problems related to predicate detection are in the parallel complexity class NC. Given a computation on n processes with at most m events per process, our parallel algorithm to detect a given conjunctive predicate takes O(logmn) time and O(mn logmn) work. The sequential algorithm takes O(mn) time. For data race detection, we give a parallel algorithm that takes O(logmn logn) time, also placing that problem in NC. This is the first work, to the best of our knowledge, that places the parallel complexity of such predicate detection problems in the class NC.