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The Generalized Rank of Trace Languages

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Developments in Language Theory (DLT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10396))

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Abstract

The notion of rank of a language with respect to an independence alphabet is generalized from concatenations of two words to an arbitrary fixed number of words. It is proved that in the case of free commutative monoids, as well as in the more general case of direct products of free monoids, sequences of ranks of regular languages are exactly non-decreasing sequences that are eventually constant. On the other hand, by uncovering a relationship between rank sequences of regular languages and rational series over the min-plus semiring, it is shown that already for free products of free commutative monoids, rank sequences need not be eventually periodic.

This work was supported by grant 15-02862S of the Czech Science Foundation.

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Acknowledgments

We are grateful to Jacques Sakarovitch and Sylvain Lombardy for pointing us to the result of Simon [9].

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37, Brno, Czech Republic

    Michal Kunc & Jan Meitner

Authors
  1. Michal Kunc
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  2. Jan Meitner
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Correspondence to Michal Kunc .

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Editors and Affiliations

  1. Université de Liège, Liège, Belgium

    Émilie Charlier

  2. Université de Liège, Liège, Belgium

    Julien Leroy

  3. Université de Liège, Liège, Belgium

    Michel Rigo

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Kunc, M., Meitner, J. (2017). The Generalized Rank of Trace Languages. In: Charlier, É., Leroy, J., Rigo, M. (eds) Developments in Language Theory. DLT 2017. Lecture Notes in Computer Science(), vol 10396. Springer, Cham. https://doi.org/10.1007/978-3-319-62809-7_18

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  • DOI: https://doi.org/10.1007/978-3-319-62809-7_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62808-0

  • Online ISBN: 978-3-319-62809-7

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