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Undecidability of the State Complexity of Composed Regular Operations

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Language and Automata Theory and Applications (LATA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6638))

Abstract

We consider the regularity-preserving operations of intersection and marked catenation and construct an infinite sequence C i , i = 1, 2, …, of compositions formed from the two operations. We construct also an infinite sequence of polynomials S i , i = 1, 2, …, with positive integer coefficients. As a main result we prove that it is undecidable whether or not S i is a state complexity function of C i . All languages needed are over a fixed alphabet with at most 50 letters. We also consider some implications and generalizations, as well as present some open problems.

This work is supported by Natural Science and Engineering Council of Canada Discovery Grants 147224 and 41630.

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References

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Author information

Authors and Affiliations

  1. Turku Centre for Computer Science, Joukahaisenkatu 3-5 B, 20520, Turku, Finland

    Arto Salomaa

  2. School of Computing, Queen’s University, Kingston, Ontario, K7L 3N6, Canada

    Kai Salomaa

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

    Sheng Yu

Authors
  1. Arto Salomaa
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  2. Kai Salomaa
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  3. Sheng Yu
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Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Avinguda Catalunya, 35, 43002, Tarragona, Spain

    Adrian-Horia Dediu  & Carlos Martín-Vide  & 

  2. Department of Informatics, Kyushu University, 744 Motooka, 819–0395, Fukuoka, Japan

    Shunsuke Inenaga

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Salomaa, A., Salomaa, K., Yu, S. (2011). Undecidability of the State Complexity of Composed Regular Operations. In: Dediu, AH., Inenaga, S., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2011. Lecture Notes in Computer Science, vol 6638. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21254-3_39

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  • DOI: https://doi.org/10.1007/978-3-642-21254-3_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21253-6

  • Online ISBN: 978-3-642-21254-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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