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Simulations over Two-Dimensional On-Line Tessellation Automata

Gérard Cécé 1 Alain Giorgetti 1, 2 
2 CASSIS - Combination of approaches to the security of infinite states systems
FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174), Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
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.
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Submitted on : Friday, November 18, 2011 - 11:29:52 AM
Last modification on : Friday, January 21, 2022 - 3:08:57 AM

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Gérard Cécé, Alain Giorgetti. Simulations over Two-Dimensional On-Line Tessellation Automata. 15th International Conference on Developments in Language Theory - DLT 2011, Jul 2011, Milan, Italy. pp.141--152, ⟨10.1007/978-3-642-22321-1_13⟩. ⟨hal-00642531⟩



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