Bit-Parallel Algorithms for Translating Regular Expressions into NFAs

Abstract

The aim of the paper is to design efficient bit-parallel algorithms for translating regular expressions into nondeterministic finite automata (NFAs). Let r be a regular expression over an alphabet Σ, and let n be the length of r and let m be the number of symbols of Σ occurring in r. Then we present bit-parallel algorithms for translating regular expressions into Glushkov automata (position automata) and follow automata using Thompson automata. For Glushkov automata, we will give an algorithm which runs in O(n + m⌈m/W⌉)time and space. For follow automata, we will give a randomized algorithm which runs in O(n + m⌈m/W⌉) expected time and O(n + m⌈m/W⌉) space. We rely on a W-bit uniform RAM for estimating the complexities of algorithms. Since the best known algorithms for these automata runs in O(n + m2) time and space, our algorithms achieve an almost W-fold speed-up.