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Complexity of Proper Suffix-Convex Regular Languages

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Implementation and Application of Automata (CIAA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10977))

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Abstract

A language L is suffix-convex if for any words u, v, w, whenever w and uvw are in L, vw is in L as well. Suffix-convex languages include left ideals, suffix-closed languages, and suffix-free languages, which were studied previously. In this paper, we concentrate on suffix-convex languages that do not belong to any one of these classes; we call such languages proper. In order to study this language class, we define a structure called a suffix-convex triple system that characterizes the automata recognizing suffix-convex languages. We find tight upper bounds for reversal, star, product, and boolean operations of proper suffix-convex languages, and we conjecture on the size of the largest syntactic semigroup. We also prove that three witness streams are required to meet all these bounds.

This work was supported by the Natural Sciences and Engineering Research Council of Canada grant No. OGP0000871, NSERC Discovery grant No. 8237-2012, and the Canada Research Chairs Program.

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Notes

  1. 1.

    This fact is offered without proof, but it is not difficult to verify.

  2. 2.

    Additionally, it is usually required that the atoms of the language are as complex as possible [4], but this measure is not discussed here.

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Authors and Affiliations

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

    Corwin Sinnamon

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  1. Corwin Sinnamon
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Correspondence to Corwin Sinnamon .

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  1. University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada

    Cezar Câmpeanu

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Sinnamon, C. (2018). Complexity of Proper Suffix-Convex Regular Languages. In: Câmpeanu, C. (eds) Implementation and Application of Automata. CIAA 2018. Lecture Notes in Computer Science(), vol 10977. Springer, Cham. https://doi.org/10.1007/978-3-319-94812-6_27

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  • DOI: https://doi.org/10.1007/978-3-319-94812-6_27

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