Space-Efficient Representations for Glushkov Automata

摘要

Glushkov automaton is an efficient structure for matching regular expressions. We present an O(k2(k)) bits space representation of Glushkov automata of regular expressions, where k is the number of strings in the regular expression. The state transition runs in time O(inverted right perpendicularm/winverted left perpendicular log k), where w is the size of machine words, and m is the number of states in the Glushkov automaton. For k = 4m/(root 8w + 9 - 1), the time is O(inverted right perpendicularm/winverted left perpendicular). Our approach is based on two operations on words that retrieve and set bits on a specific set of positions of a word. We present implementations of these operations using bit-parallelism and a permutation network, which are simple and efficient.