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Deterministic Two-Dimensional Languages over One-Letter Alphabet

  • Marcella Anselmo
  • Maria Madonia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4728)

Abstract

We study the family DREC(1) of deterministic tiling recognizable two-dimensional languages in the case of a one-letter alphabet. The family coincides with both the class of languages accepted by deterministic on-line tessellation acceptors (\(\mathcal{L}\)(DOTA)(1)) and the one of languages recognized by 2-way alternating finite automata (\(\mathcal{L}\)(2AFA)(1)). We show that DREC(1) is complex enough to contain languages that cannot be realized by classical operations, while other languages constructed using classical operations cannot be deterministically recognized. Furthermore we prove that there are unambiguously recognizable languages that cannot be deterministically recognized even in the case of one-letter alphabet. In particular \(\mathcal{L}\)(DOTA)(1) is different from \(\mathcal{L}\)(OTA)(1) (its non-deterministic counterpart).

Keywords

Automata and Formal Languages Determinism Two-dimensional languages 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Marcella Anselmo
    • 1
  • Maria Madonia
    • 2
  1. 1.Dipartimento di Informatica ed Applicazioni, Università di Salerno I-84084 Fisciano (SA)Italy
  2. 2.Dip. Matematica e Informatica, Università di Catania, Viale Andrea Doria 6/a, 95125 CataniaItaly

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