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The regular languages of wire linear AC\(^0\)

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Abstract

In this paper, the regular languages of wire linear \(\hbox {AC}^0\)are characterized as the languages expressible in the two-variable fragment of first-order logic with regular predicates, \(\mathrm{FO}^2[\mathrm{reg}]\). Additionally, they are characterized as the languages recognized by the algebraic class \(\mathbf {QLDA}\). The class is shown to be decidable and examples of languages in and outside of it are presented.

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Notes

  1. For the reader familiar with algebraic language theory: note that to simplify presentation, we do not define varieties of monoids and see them as varieties of stamps.

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Acknowledgements

We thank Luc Dartois who contributed to some of the proofs in this paper, Corentin Barlois for expert proofreading, and the reviewers for interesting comments. Above all, we thank Klaus–Jörn for a fantastic few years in Tübingen and send him heartfelt birthday wishes for his 70th—and to many more!

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Authors and Affiliations

  1. School of Computing, DePaul University, 243 S. Wabash Ave., Chicago, IL, 60604, USA

    Michaël Cadilhac

  2. Inria LINKS Team & University of Lille, 40 avenue Halley, 59000, Villeneuve d’Ascq, France

    Charles Paperman

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  1. Michaël Cadilhac
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Correspondence to Michaël Cadilhac or Charles Paperman.

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Cadilhac, M., Paperman, C. The regular languages of wire linear AC\(^0\). Acta Informatica 59, 321–336 (2022). https://doi.org/10.1007/s00236-022-00432-2

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