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\(+\omega \)-Picture Languages Recognizable by Büchi-Tiling Systems

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Language and Automata Theory and Applications (LATA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9618))

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Abstract

We consider \(+\omega \)-pictures, i.e., 2-dimensional pictures with a finite number of rows and a countably infinite number of columns. We extend conventional tiling systems with a Büchi acceptance condition and define the class of Büchi-tiling recognizable \(+\omega \)-picture languages. We show that this class has the same closure properties as the class of tiling recognizable languages of finite pictures. We characterize the class of Büchi-tiling recognizable \(+\omega \)-picture languages by generalized Büchi-tiling systems and by the logic \(\text {EMSO}^\infty \), an extension of existential monadic second-order logic with quantification of infinite sets. The Büchi characterization theorem (stating that the \(\omega \)-regular languages are finite unions of languages of the form \(L_1\cdot L_2^\omega \), for regular languages \(L_1\) and \(L_2\)), however, does not carry over from regular \(\omega \)-languages to Büchi-tiling recognizable languages of \(+\omega \)-pictures.

P. Babari—Supported by DFG Graduiertenkolleg 1763 (QuantLA)

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Authors and Affiliations

  1. Institut für Informatik, Universität Leipzig, Leipzig, Germany

    Parvaneh Babari

  2. Institut für Informatik, Humboldt-Universität zu Berlin, Berlin, Germany

    Nicole Schweikardt

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  1. Parvaneh Babari
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  2. Nicole Schweikardt
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Correspondence to Nicole Schweikardt .

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Editors and Affiliations

  1. Rovira i Virgili University, Tarragona, Spain

    Adrian-Horia Dediu

  2. Czech Technical University, Prague, Czech Republic

    Jan Janoušek

  3. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  4. Justus Liebig University Giessen, Gießen, Germany

    Bianca Truthe

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Babari, P., Schweikardt, N. (2016). \(+\omega \)-Picture Languages Recognizable by Büchi-Tiling Systems. In: Dediu, AH., Janoušek, J., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2016. Lecture Notes in Computer Science(), vol 9618. Springer, Cham. https://doi.org/10.1007/978-3-319-30000-9_6

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  • DOI: https://doi.org/10.1007/978-3-319-30000-9_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-29999-0

  • Online ISBN: 978-3-319-30000-9

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