An improved algorithm for the membership problem for extended regular expressions

Orna Kupferman, Sharon Zuhovitzky

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

15 Scopus citations

Abstract

Extended regular expressions (ERE) define regular languages using union, concatenation, repetition, intersection, and complementation operators. The fact ERE allow intersection and complementation makes them exponentially more succinct than regular expressions. The membership problem for extended regular expressions is to decide, given an expression r and a word w, whether w belongs to the language defined by r. Since regular expressions are useful for describing patterns in strings, the membership problem has numerous applications. In many such applications, the words w are very long and patterns are conveniently described using ERE, making efficient solutions to the membership problem of great practical interest. In this paper we introduce alternating automata with synchronized universality and negation, and use them in order to obtain a simple and efficient algorithm for solving the membership problem for ERE. Our algorithm runs in time O(m ・ n2) and space O(m ・ n + k ・ n2), where m is the length of r, n is the length of w, and k is the number of intersection and complementation operators in r. This improves the best known algorithms for the problem.

Original languageAmerican English
Title of host publicationMathematical Foundations of Computer Science 2002 - 27th International Symposium, MFCS 2002, Proceedings
EditorsKrzysztof Diks, Wojciech Rytter, Wojciech Rytter
PublisherSpringer Verlag
Pages446-458
Number of pages13
ISBN (Print)3540440402, 9783540440406
DOIs
StatePublished - 2002
Event27th International Symposium on Mathematical Foundations of Computer Science, MFCS 2002 - Warsaw, Poland
Duration: 26 Aug 200230 Aug 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2420
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference27th International Symposium on Mathematical Foundations of Computer Science, MFCS 2002
Country/TerritoryPoland
CityWarsaw
Period26/08/0230/08/02

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.

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