A New Translation from Semi-extended Regular Expressions into NFAs and Its Application to an Approximate Matching Problem

Abstract

Semi-extended regular expressions (SEREs) are regular expressions (REs) with intersection. Two algorithms for translating REs into nondeterministic finite automata (NFAs) are widely known, that is, Thompson construction and Glushkov construction. A trivial way for translating SEREs into NFAs is to use Thompson construction because it can easily be applied to SEREs. It seems to be difficult to directly apply Glushkov construction to SEREs. In this paper, we present a new translation from SEREs into NFAs using Glushkov construction and the modular decomposition technique by Yamamoto. Then, given an SERE r with m r intersection operators, we can generate an NFA with at most N r +1 states and \(N^2_r\) transitions in \(O((m_r + 1)N^2_r)\) time and space. Here N r is a number obtained from the decomposition of r, and is less than the number of states of an NFA obtained by the trivial translation (that is, the translation using Thompson construction). In addition, we will show an application to an approximate SERE matching problem.