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Derivatives and Finite Automata of Expressions in Star Normal Form

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Language and Automata Theory and Applications (LATA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10168))

Abstract

This paper studies derivatives and automata for expressions in star normal form as defined by Brüggemann-Klein. For an expression in star normal form, the paper shows that the derivatives are either \(\emptyset \) or unique, while in general Berry and Sethi’s result shows the derivatives are either \(\emptyset \) or similar. It is known that the partial derivative automaton and the follow automaton are two small automata, each of which is a quotient of the position automaton. For the relation between the partial derivative and follow automata, however, Ilie and Yu stated that a rigorous analysis is necessary but difficult. The paper tackles the issue, and presents several results. Our work shows that there are different conditions under which the relation of the two automata can be different.

Work supported by the National Natural Science Foundation of China under Grant No. 61472405.

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Notes

  1. 1.

    This quotient result, however, is not given in [6]. In [6] the main theorem (Theorem 4, p.11) states for a “normalized” regular expression, the size of the partial derivative automaton is smaller than the size of the follow automaton.

  2. 2.

    \(RF=\{EF | E\in R\}\) for a set R of regular expressions and a regular expression F.

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Author information

Authors and Affiliations

  1. State Key Laboratory of Computer Science, Institute of Software Chinese Academy of Sciences, Beijing, 100190, China

    Haiming Chen

  2. BDBC, Beihang University, Beijing, 100191, China

    Ping Lu

Authors
  1. Haiming Chen
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  2. Ping Lu
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Correspondence to Haiming Chen .

Editor information

Editors and Affiliations

  1. Umeå University, Umeå, Sweden

    Frank Drewes

  2. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  3. University of Giessen, Giessen, Germany

    Bianca Truthe

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Chen, H., Lu, P. (2017). Derivatives and Finite Automata of Expressions in Star Normal Form. In: Drewes, F., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2017. Lecture Notes in Computer Science(), vol 10168. Springer, Cham. https://doi.org/10.1007/978-3-319-53733-7_17

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  • DOI: https://doi.org/10.1007/978-3-319-53733-7_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53732-0

  • Online ISBN: 978-3-319-53733-7

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