An automata-based recognition algorithm for semi-extended regular expressions

Abstract

This paper is concerned with the recognition problem for semi-extended regular expressions: given a semi-extended regular expression r of length m and an input string x of length n, determine if x ∈ L(r), where L(r) denotes the language denoted by r. Although the recognition algorithm based on nondeterministic finite automata (NFAs) for regular expressions is widely known, a similar algorithm based on finite automata is currently not known for semi-extended regular expressions. The existing algorithm is based on dynamic programming. We here present an efficient automata-based recognition algorithm by introducing a new model of alternating finite automata called partially input-synchronized alternating finite automata (PISAFAs for short). Our algorithm based on PISAFAs runs in O(mn2) time and O(mn + kn2) space, though the existing algorithm based on dynamic programming runs in O(mn3) time and O(mn2) space, where k is the number of intersection operators occurring in r. Thus our algorithm significantly improves the existing one.