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International Conference on Implementation and Application of Automata

CIAA 2022: Implementation and Application of Automata pp 80–92Cite as

A Similarity Measure for Formal Languages Based on Convergent Geometric Series

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Part of the Lecture Notes in Computer Science book series (LNCS,volume 13266)

Abstract

We present a distance metric on formal languages based on the accumulated weight of words in their symmetric difference. The contribution of an individual word to this weight decreases exponentially in its length, guaranteeing the distance between languages to be a real value between 0 and 1. We show that this distance is computable for regular languages. As an application, we show how the similarity measure derived from a modification of this metric can be used in automatic grading of particular standard exercises in formal language theory classes.

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Fig. 1.

Notes

  1. 1.

    Actual matrix multiplication can be done in time \(\mathcal {O}(|Q|^{2.37286})\), cf. e.g. [1]. We state the cubic runtime here for the sake of readability.

  2. 2.

    https://github.com/maurice-herwig/wofa.git.

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Authors and Affiliations

  1. University of Kassel, Kassel, Germany

    Florian Bruse, Maurice Herwig & Martin Lange

Authors
  1. Florian Bruse
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  2. Maurice Herwig
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  3. Martin Lange
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Corresponding author

Correspondence to Florian Bruse .

Editor information

Editors and Affiliations

  1. UFR. des Sciences et Techniques, University of Rouen, Saint-Étienne du Rouvray Cedex, France

    Pascal Caron

  2. UFR. des Sciences et Techniques, University of Rouen, Saint-Étienne du Rouvray Cedex, France

    Ludovic Mignot

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Bruse, F., Herwig, M., Lange, M. (2022). A Similarity Measure for Formal Languages Based on Convergent Geometric Series. In: Caron, P., Mignot, L. (eds) Implementation and Application of Automata. CIAA 2022. Lecture Notes in Computer Science, vol 13266. Springer, Cham. https://doi.org/10.1007/978-3-031-07469-1_6

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  • DOI: https://doi.org/10.1007/978-3-031-07469-1_6

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