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On the State Complexity of Complements, Stars, and Reversals of Regular Languages

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Developments in Language Theory (DLT 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5257))

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Abstract

We examine the deterministic and nondeterministic state complexity of complements, stars, and reversals of regular languages. Our results are as follows:

  1. 1

    The nondeterministic state complexity of the complement of an n-state NFA language over a five-letter alphabet may reach each value in the range from logn to 2n.

  2. 1

    The state complexity of the star (reversal) of an n-state DFA language over a growing alphabet may reach each value in the range from 1 to \(\frac{3}{4}2^n\) (from logn to 2n, respectively).

  3. 1

    The nondeterministic state complexity of the star (reversal) of an n-state NFA binary language may reach each value in the range from 1 to n + 1 (from n − 1 to n + 1, respectively).

We also obtain some partial results on the nondeterministic state complexity of the complements of binary regular languages. As a bonus, we get an exponential number of values that are non-magic, which improves a similar result of Geffert (Proc. 7th DCFS, Como, Italy, 23–37).

Research supported by the VEGA grant 2/6089/26.

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  1. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01, Košice, Slovakia

    Galina Jirásková

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  1. Galina Jirásková
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Masami Ito Masafumi Toyama

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Jirásková, G. (2008). On the State Complexity of Complements, Stars, and Reversals of Regular Languages. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2008. Lecture Notes in Computer Science, vol 5257. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85780-8_34

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  • DOI: https://doi.org/10.1007/978-3-540-85780-8_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85779-2

  • Online ISBN: 978-3-540-85780-8

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