Extended to Multi-Tilde-Bar Regular Expressions and Efficient Finite Automata Constructions

摘要

Several algorithms have been designed to convert a regular expression into anequivalent finite automaton. One of the most popular constructions, due toGlushkov and to McNaughton and Yamada, is based on the computation of the Null,First, Last and Follow sets (called Glushkov functions) associated with alinearized version of the expression. Recently Mignot considered a family ofextended expressions called Extended to multi-tilde-bar Regular Expressions(EmtbREs) and he showed that, under some restrictions, Glushkov functions canbe defined for an EmtbRE. In this paper we present an algorithm whichefficiently computes the Glushkov functions of an unrestricted EmtbRE. Ourapproach is based on a recursive definition of the language associated with anEmtbRE which enlightens the fact that the worst case time complexity of theconversion of an EmtbRE into an automaton is related to the worst case timecomplexity of the computation of the Null function. Finally we show how toextend the ZPC-structure to EmtbREs, which allows us to apply to this family ofextended expressions the efficient constructions based on this structure (inparticular the construction of the c-continuation automaton, the positionautomaton, the follow automaton and the equation automaton).