Simulations over two-dimensional on-line tessellation automata

Authors:
Gérard Cécé;Alain Giorgetti
Affiliations:
LIFC, University of Franche-Comté, France and Centre Numerica, Montbeliard Cedex;LIFC, University of Franche-Comté, France and INRIA, CASSIS, Besancon Cedex
Venue:
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Year:
2011

Citing 8
Cited 0

Two-dimensional languages

Handbook of formal languages, vol. 3
Simulation-based minimization

ACM Transactions on Computational Logic (TOCL)
Uniform and nonuniform recognizability

Theoretical Computer Science
Picture Languages: From Wang Tiles to 2D Grammars

CAI '09 Proceedings of the 3rd International Conference on Algebraic Informatics
A computational model for tiling recognizable two-dimensional languages

Theoretical Computer Science
An algebraic definition of simulation between programs

IJCAI'71 Proceedings of the 2nd international joint conference on Artificial intelligence
Computing simulations over tree automata: efficient techniques for reducing tree automata

TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
When simulation meets antichains: on checking language inclusion of nondeterministic finite (tree) automata

TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems

Quantified Score

Hi-index	0.00

Visualization

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.