An optimal parallel algorithm for learning DFA

Abstract

In 1987, D. Angluin presented an algorithm that exactly learns regular languages represented by deterministic finite automata (dfa) from Membership and Equivalence queries. Furthermore, the algorithm is feasible in the sense that it takes time O(n^2m^2), where n is the number of states of the automaton and m is the length of the longest counterexample to an Equivalence query. This paper studies whether parallelism can lead to substantially more efficient algorithms for the problem. We show that no CRCW PRAM machine using a number of processors polynomial in n and m can identify dfa in o(n/log n) time. Furthermore, this lower bound is tight: we develop a CRCW PRAM learning algorithm that uses polynomially many processors and exactly learns dfa in O(n/log n) time.