InforLorV4, Main, Exploration, bibRecord, 002219

Simulations over Two-Dimensional On-Line Tessellation Automata

Identifieur interne : 002219 ( Main/Exploration ); précédent : 002218; suivant : 002220

Simulations over Two-Dimensional On-Line Tessellation Automata

Auteurs : Gérard Cécé [France] ; Alain Giorgetti [France]

Source :

RBID : Hal:hal-00642531

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.

Url:

https://hal.inria.fr/hal-00642531

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

Affiliations:

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Le document en format XML

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<front><div type="abstract" xml:lang="en">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.</div>
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Simulations over Two-Dimensional On-Line Tessellation Automata

Simulations over Two-Dimensional On-Line Tessellation Automata

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Abstract

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Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri