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Most Complex Regular Right-Ideal Languages

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Descriptional Complexity of Formal Systems (DCFS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8614))

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Abstract

A right ideal is a language L over an alphabet Σ that satisfies the equation L = LΣ*. We show that there exists a sequence (\(R_n \mid n \geqslant 3\)) of regular right-ideal languages, where R n has n left quotients and is most complex among regular right ideals under the following measures of complexity: the state complexities of the left quotients, the number of atoms (intersections of complemented and uncomplemented left quotients), the state complexities of the atoms, the size of the syntactic semigroup, the state complexities of reversal, star, product, and all binary boolean operations that depend on both arguments. Thus (\(R_n \mid n \geqslant 3\)) is a universal witness reaching the upper bounds for these measures.

This work was supported by the Natural Sciences and Engineering Research Council of Canada under grant No. OGP0000871.

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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. Department of Pure Mathematics, University of Waterloo, Waterloo, ON, Canada, N2L 3G1

    Gareth Davies

Authors
  1. Janusz Brzozowski
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  2. Gareth Davies
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Editor information

Editors and Affiliations

  1. Department of Computer Science, The University of Western Ontario, N6A 5B7, London, Ontario, Canada

    Helmut Jürgensen

  2. Department of Mathematics and TUCS, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  3. University of Turku, Fi-20014, Turku, Finland

    Alexander Okhotin

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Brzozowski, J., Davies, G. (2014). Most Complex Regular Right-Ideal Languages. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds) Descriptional Complexity of Formal Systems. DCFS 2014. Lecture Notes in Computer Science, vol 8614. Springer, Cham. https://doi.org/10.1007/978-3-319-09704-6_9

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  • DOI: https://doi.org/10.1007/978-3-319-09704-6_9

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09703-9

  • Online ISBN: 978-3-319-09704-6

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