Simulations over Two-Dimensional On-Line Tessellation Automata

  • Gérard Cécé
  • Alain Giorgetti
Conference paper

DOI: 10.1007/978-3-642-22321-1_13

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6795)
Cite this paper as:
Cécé G., Giorgetti A. (2011) Simulations over Two-Dimensional On-Line Tessellation Automata. In: Mauri G., Leporati A. (eds) Developments in Language Theory. DLT 2011. Lecture Notes in Computer Science, vol 6795. Springer, Berlin, Heidelberg

Abstract

We study the notion of simulation over a class of automata which recognize 2D languages (languages of arrays of letters). This class of two-dimensional On-line Tessellation Automata (2OTA) accepts the same class of languages as the class of tiling systems, considered as the natural extension of classical regular word languages to the 2D case. We prove that simulation over 2OTA implies language inclusion. Even if the existence of a simulation relation between two 2OTA is shown to be a NP-complete problem in time, this is an important result since the inclusion problem is undecidable in general in this class of languages. Then we prove the existence of a unique maximal autosimulation relation in a given 2OTA and the existence of a unique minimal 2OTA which is simulation equivalent to this given 2OTA, both computable in polynomial time.

Keywords

Simulation 2D words Tiling systems Picture languages Picture automata 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Gérard Cécé
    • 1
    • 2
  • Alain Giorgetti
    • 1
    • 3
  1. 1.LIFC - EA 4269 - University of Franche-ComtéFrance
  2. 2.Centre Numerica, 1 cours Leprince-RinguetMONTBELIARD CedexFrance
  3. 3.INRIA/CASSISBESANCON CedexFrance

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