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State Complexity Investigations on Commutative Languages – the Upward and Downward Closure, Commutative Aperiodic and Commutative Group Languages

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Descriptional Complexity of Formal Systems (DCFS 2021)

Abstract

We investigate the state complexity of the upward and downward closure and interior operations on commutative regular languages. Then, we systematically study the state complexity of these operations and of the shuffle operation on commutative group languages and commutative aperiodic (or star-free) languages.

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Notes

  1. 1.

    Over the whole alphabet \(\varSigma \), these languages are precisely the languages recognizable by automata whose transition monoids are 0-groups, i.e., groups with a zero element adjoined.

  2. 2.

    Also called a scattered subword in the literature [9, 19].

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Acknowledgement

I thank the anonymous referees of [14] (the extended version of [15]) whose feedback also helped in the present work. I also thank the referees of the present work for critical and careful reading, and pointing out typos and parts that needed better explanation.

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Hoffmann, S. (2021). State Complexity Investigations on Commutative Languages – the Upward and Downward Closure, Commutative Aperiodic and Commutative Group Languages. In: Han, YS., Ko, SK. (eds) Descriptional Complexity of Formal Systems. DCFS 2021. Lecture Notes in Computer Science(), vol 13037. Springer, Cham. https://doi.org/10.1007/978-3-030-93489-7_6

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  • DOI: https://doi.org/10.1007/978-3-030-93489-7_6

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