Brief Announcement: Regular and Dyck Languages in MPC

Regular languages are some of the most widely studied languages in computer science history. Given a regular language L ⊆ {0, 1} ⋆ and string ω ∈ {0, 1} ⋆, two of the most fundamental regular language problems are recognition, the problem of determining if w is in L, and testing, the problem of determining if w is at most ε-far from L. In this paper we modernize regular language recognition and testing algorithms for the Massively Parallel Computations (MPC) model used everyday in big data engineering. First we give a regular language testing algorithm, which succeeds with high probability using Õ(1 over ε) queries to the input string. Following the testing algorithm, we give a simple dynamic programming solution for regular language recognition. Both algorithms run in constant communication rounds and O(n) total memory in MPC where n is the size of the input.