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Upper Bounds on Syntactic Complexity of Left and Two-Sided Ideals

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Developments in Language Theory (DLT 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8633))

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Abstract

We solve two open problems concerning syntactic complexity. We prove that the cardinality of the syntactic semigroup of a left ideal or a suffix-closed language with n left quotients (that is, with state complexity n) is at most n n − 1 + n − 1, and that of a two-sided ideal or a factor-closed language is at most n n − 2 + (n − 2)2n − 2 + 1. Since these bounds are known to be reachable, this settles the problems.

This work was supported by the Natural Sciences and Engineering Research Council of Canada grant No. OGP000087, and by Polish NCN grant DEC-2013/09/N/ST6/01194.

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References

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Author information

Authors and Affiliations

  1. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada, N2L 3G1

    Janusz Brzozowski

  2. Institute of Computer Science, University of Wrocław, Joliot-Curie 15, PL-50-383, Wrocław, Poland

    Marek Szykuła

Authors
  1. Janusz Brzozowski
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  2. Marek Szykuła
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Editor information

Editors and Affiliations

  1. Institute of Mathematics and Computer Science, Ural Federal University, pr. Lenina, 51, 620000, Ekaterinburg, Russia

    Arseny M. Shur  & Mikhail V. Volkov  & 

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Brzozowski, J., Szykuła, M. (2014). Upper Bounds on Syntactic Complexity of Left and Two-Sided Ideals. In: Shur, A.M., Volkov, M.V. (eds) Developments in Language Theory. DLT 2014. Lecture Notes in Computer Science, vol 8633. Springer, Cham. https://doi.org/10.1007/978-3-319-09698-8_2

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  • DOI: https://doi.org/10.1007/978-3-319-09698-8_2

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09697-1

  • Online ISBN: 978-3-319-09698-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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