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New Results on Alternating and Non-deterministic Two-Dimensional Finite-State Automata

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STACS 2001 (STACS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2010))

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Abstract

We resolve several long-standing open questions regarding the power of various types of finite-state automata to recognize “pic- ture languages,” i.e. sets of two-dimensional arrays of symbols. We show that the languages recognized by 4-way alternating finite-state automata (AFAs) are incomparable to the so-called tiling recognizable languages. Specifically, we show that the set of acyclic directed grid graphs with crossover is AFA-recognizable but not tiling recognizable, while its com- plement is tiling recognizable but not AFA-recognizable. Since we also show that the complement of an AFA-recognizable language is tiling rec- ognizable, it follows that the AFA-recognizable languages are not closed under complementation. In addition, we show that the set of languages recognized by 4-way NFAs is not closed under complementation, and that NFAs are more powerful than DFAs, even for languages over one symbol.

Research supported by NSF Grant CCR 97-33101.

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Author information

Authors and Affiliations

  1. Department of Computer Science, 15 MLH, University of Iowa, 52242, Iowa City, IA, USA

    Jarkko Kari

  2. Computer Science Department and Department of Physics and Astronomy, University of New Mexico, 87131, Albuquerque, NM

    Cristopher Moore

Authors
  1. Jarkko Kari
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  2. Cristopher Moore
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Editor information

Editors and Affiliations

  1. I3S & INRIA Sophia Antipolis INRIA, CNRS, 2004 Route des Lucioles, 06902, Sophia-Antipolis, France

    Afonso Ferreira

  2. Institut für Theoretische Informatik, Fakultät Informatik, TU Dresden, 01062, Dresden, Germany

    Horst Reichel

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© 2001 Springer-Verlag Berlin Heidelberg

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Kari, J., Moore, C. (2001). New Results on Alternating and Non-deterministic Two-Dimensional Finite-State Automata. In: Ferreira, A., Reichel, H. (eds) STACS 2001. STACS 2001. Lecture Notes in Computer Science, vol 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44693-1_35

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  • DOI: https://doi.org/10.1007/3-540-44693-1_35

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41695-1

  • Online ISBN: 978-3-540-44693-4

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