Computing the equation automaton of a regular expression in O(s2) space and time

Abstract

Let E be a regular expression the size of which is s. Mirkin's prebases and Antimirov's partial derivatives lead to the construction of the same automaton, called the equation automaton of E. The number of states in this automaton is less than or equal to the number of states in the position automaton. On the other hand, it can be computed by Antimirov's algorithm with an O(s5) time complexity, whereas there exist O(s2) implementations for the position automaton. We present an O(s2) space and time algorithm to compute the equation automaton. It is based on the notion of canonical derivative which is related both to word and partial derivatives. This work is tightly connected to pattern matching area since the aim is, given a regular expression, to produce an as small as possible recognizer with the best space and time complexity.