Extended to multi-tilde–bar regular expressions and efficient finite automata constructions

Abstract

Several algorithms have been designed to convert a regular expression into an equivalent finite automaton. One of the most popular constructions, due to Glushkov and to McNaughton and Yamada, is based on the computation of the Null, First, Last and Follow sets (called Glushkov functions) associated with a linearized version of the expression. Recently Mignot considered a family of extended expressions called Extended to multi-tilde–bar Regular Expressions (EmtbREs) and he showed that, under some restrictions, Glushkov functions can be defined for an EmtbRE. In this paper we present an algorithm which efficiently computes the Glushkov functions of an unrestricted EmtbRE. Our approach is based on a recursive definition of the language associated with an EmtbRE which enlightens the fact that the worst case time complexity of the conversion of an EmtbRE into an automaton is related to the worst case time complexity of the computation of the Null function. Finally we show how to extend the ZPC-structure to EmtbREs, which allows us to apply to this family of extended expressions the efficient constructions based on this structure (in particular the construction of the c-continuation automaton, the position automaton, the follow automaton and the equation automaton).