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Shuffle Product of Regular Languages: Results and Open Problems

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Algebraic Informatics (CAI 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13706))

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Abstract

This survey paper presents known results and open problems on the shuffle product applied to regular languages. We first focus on varieties and positive varieties closed under shuffle. Next we turn to the class of intermixed languages, the smallest class of languages containing the letters and closed under Boolean operations, product and shuffle. Finally, we study Schnoebelen’s sequential and parallel decompositions of languages and discuss various open questions around this notion.

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Notes

  1. 1.

    The syntactic ordered monoid of a language was first introduced by Schützenberger in 1956, but he apparently only made use of the syntactic monoid later on. I rediscovered this notion in 1995 [11], but unfortunately used the opposite order for several years, in particular in [3,4,5,6], before I switched back to the original order.

  2. 2.

    As explained in the first footnote, the opposite of the syntactic order was used in this paper, and consequently, upper set monoids were used in place of lower set monoids.

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Authors and Affiliations

  1. IRIF, CNRS and Université Paris-Cité, Case 7014, 75205, Paris Cedex 13, France

    Jean-Éric Pin

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  1. Jean-Éric Pin
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Correspondence to Jean-Éric Pin .

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Editors and Affiliations

  1. Aristotle University of Thessaloniki, Thessaloniki, Greece

    Dimitrios Poulakis

  2. Aristotle University of Thessaloniki, Thessaloniki, Greece

    George Rahonis

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Pin, JÉ. (2022). Shuffle Product of Regular Languages: Results and Open Problems. In: Poulakis, D., Rahonis, G. (eds) Algebraic Informatics. CAI 2022. Lecture Notes in Computer Science, vol 13706. Springer, Cham. https://doi.org/10.1007/978-3-031-19685-0_3

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  • DOI: https://doi.org/10.1007/978-3-031-19685-0_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-19684-3

  • Online ISBN: 978-3-031-19685-0

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