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Annual Symposium on Combinatorial Pattern Matching

CPM 2001: Combinatorial Pattern Matching pp 157–168Cite as

Computing the Equation Automaton of a Regular Expression in O(s 2) Space and Time

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2089))

Abstract

Let E be a regular expression the size of which is s. Mirkin’s prebases and Antimirov’s partial derivatives lead to the construction of the same automaton, called the equation automaton of E. The number of states in this automaton is less than or equal to the number of states in the position automaton. On the other hand, it can be computed by Antimirov’s algorithm with an O(s 5) time complexity, whereas there exist O(s 2) implementations for the position automaton. We present an O(s 2) space and time algorithm to compute the equation automaton. It is based on the notion of canonical derivative which is related both to word and partial derivatives. This work is tightly connected to pattern matching area since the aim is, given a regular expression, to produce an as small as possible recognizer with the best space and time complexity.

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Author information

Authors and Affiliations

  1. LIFAR, Université de Rouen, 76821, Mont-Saint-Aignan Cedex, France

    Jean-Marc Champarnaud

Authors
  1. Jean-Marc Champarnaud
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  2. Djelloul Ziadi
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Bar-Ilan University, 52900, Ramat-Gan, Israel, Atlanta, Georgia, 30332-0280, USA

    Amihood Amir

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Champarnaud, JM., Ziadi, D. (2001). Computing the Equation Automaton of a Regular Expression in O(s 2) Space and Time. In: Amir, A. (eds) Combinatorial Pattern Matching. CPM 2001. Lecture Notes in Computer Science, vol 2089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48194-X_15

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  • DOI: https://doi.org/10.1007/3-540-48194-X_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42271-6

  • Online ISBN: 978-3-540-48194-2

  • eBook Packages: Springer Book Archive

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