An Effective Algorithm for the Membership Problem for Extended Regular Expressions

By adding the complement operator (¬), extended regular expressions (ERE ) can encode regular languages non-elementarily more succinctly than regular expressions. The ERE membership problem asks whether a word w of size n belongs to the language of an ERE R of size m. Unfortunately, the best known membership algorithms are either non-elementary in m or otherwise require space Ω(n) and time Ω(n); since in many practical applications n can be very large, these space and time requirements could be prohibitive. In this paper we present an ERE membership algorithm that runs in space O(n · (log n+m) · 2) and time O(n · (log n + m) · 2). The presented algorithm outperforms the best known algorithms when n is exponentially larger than m.