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, the set of decision problems decidable in polylogarithmic time on a parallel computer with a polynomial number of processors. Given a computation on n processes with at most m local states per process, our parallel algorithm to detect a given conjunctive predicate takes O(log mn) time and O(m3n3 log mn) work. The sequential algorithm takes O(mn2) time. For data race detection, we give a parallel algorithm that takes O(log mn log n) 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.