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Solving of Regular Equations Revisited

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Theoretical Aspects of Computing – ICTAC 2019 (ICTAC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11884))

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Abstract

Solving of regular equations via Arden’s Lemma is folklore knowledge. We first give a concise algorithmic specification of all elementary solving steps. We then discuss a computational interpretation of solving in terms of coercions that transform parse trees of regular equations into parse trees of solutions. Thus, we can identify some conditions on the shape of regular equations under which resulting solutions are unambiguous. We apply our result to convert a DFA to an unambiguous regular expression. In addition, we show that operations such as subtraction and shuffling can be expressed via some appropriate set of regular equations. Thus, we obtain direct (algebraic) methods without having to convert to and from finite automaton.

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Notes

  1. 1.

    http://arxiv.org/abs/1908.03710.

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Acknowledgments

We thank referees for CIAA’18, ICTAC’18 and ICTAC’19 for their helpful comments on previous versions of this paper.

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Authors and Affiliations

  1. Karlsruhe University of Applied Sciences, Karlsruhe, Germany

    Martin Sulzmann

  2. Nanyang Polytechnic, Singapore, Singapore

    Kenny Zhuo Ming Lu

Authors
  1. Martin Sulzmann
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  2. Kenny Zhuo Ming Lu
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Correspondence to Martin Sulzmann .

Editor information

Editors and Affiliations

  1. University of Sheffield, Sheffield, UK

    Robert Mark Hierons

  2. University of Bordeaux, Talence, France

    Mohamed Mosbah

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Sulzmann, M., Lu, K.Z.M. (2019). Solving of Regular Equations Revisited. In: Hierons, R., Mosbah, M. (eds) Theoretical Aspects of Computing – ICTAC 2019. ICTAC 2019. Lecture Notes in Computer Science(), vol 11884. Springer, Cham. https://doi.org/10.1007/978-3-030-32505-3_22

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  • DOI: https://doi.org/10.1007/978-3-030-32505-3_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-32504-6

  • Online ISBN: 978-3-030-32505-3

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