Article

Simulations over two-dimensional on-line tessellation automata

Authors:

Gérard Cécé,

Alain GiorgettiAuthors Info & Claims

DLT'11: Proceedings of the 15th international conference on Developments in language theory

Pages 141 - 152

Published: 19 July 2011 Publication History

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.

References

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Abdulla, P.A., Bouajjani, A., Holík, L., Kaati, L., Vojnar, T.: Computing Simulations over Tree Automata. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 93-108. Springer, Heidelberg (2008).

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Abdulla, P.A., Chen, Y.F., Holík, L., Mayr, R., Vojnar, T.:When Simulation Meets Antichains. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 158-174. Springer, Heidelberg (2010).

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Abdulla, P.A., Legay, A., d'Orso, J., Rezine, A.: Tree regular model checking: A simulation-based approach. J. Log. Algebr. Program. 69(1-2), 93-121 (2006).

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Anselmo, M., Giammarresi, D., Madonia, M.: A computational model for tiling recognizable two-dimensional languages. Theor. Comput. Sci. 410(37), 3520-3529 (2009).

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Bustan, D., Grumberg, O.: Simulation-based minimization. ACM Trans. Comput. Logic 4(2), 181-206 (2003).

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Cécé, G., Giorgetti, A.: Simulations for a Class of Two-Dimensional Automata. Research Report RR-7425, INRIA (October 2010), http://hal.inria.fr/inria-00527077/en/

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Cherubini, A., Pradella, M.: Picture Languages: FromWang Tiles to 2D Grammars. In: Bozapalidis, S., Rahonis, G. (eds.) CAI 2009. LNCS, vol. 5725, pp. 13-46. Springer, Heidelberg (2009).

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Giammarresi, D., Restivo, A.: Two-Dimensional Languages. In: Salomaa, A., Rozenberg, G. (eds.) Handbook of Formal Languages, Beyond Words, vol. 3, pp. 215-267. Springer, Berlin (1997).

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Inoue, K., Nakamura, A.: Some properties of two-dimensional on-line tessellation acceptors. Inf. Sci. 13(2), 95-121 (1977).

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Lonati, V., Pradella, M.: Deterministic recognizability of picture languages with Wang automata. Discrete Math. & Theor. Comput. Sci. 12(4), 73-94 (2010).

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Milner, R.: An Algebraic Definition of Simulation Between Programs. In: IJCAI, pp. 481-489 (1971).

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Digital Library

Cited By

Cécé GAceto LIngólfsdóttir A(2017)Foundation for a series of efficient simulation algorithmsProceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3329995.3330004(1-12)Online publication date: 20-Jun-2017
https://dl.acm.org/doi/10.5555/3329995.3330004

Index Terms

Simulations over two-dimensional on-line tessellation automata
1. Theory of computation
  1. Formal languages and automata theory
    1. Formalisms
      1. Algebraic language theory
    2. Grammars and context-free languages
  2. Models of computation

Index terms have been assigned to the content through auto-classification.

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Information

Published In

cover image Guide Proceedings

DLT'11: Proceedings of the 15th international conference on Developments in language theory

July 2011

481 pages

ISBN:9783642223204

Editors:
Giancarlo Mauri
Università degli Studi di Milano-Bicocca, Dipartimento di Informatica, Sistemistica e Comunicazione, Milano, Italy
,
Alberto Leporati
Università degli Studi di Milano-Bicocca, Dipartimento di Informatica, Sistemistica e Comunicazione, Milano, Italy

Sponsors

EATCS: European Association for Theoretical Computer Science
The University of Milano-Bicocca: The University of Milano-Bicocca

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 19 July 2011

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Citations

Cited By

Cécé GAceto LIngólfsdóttir A(2017)Foundation for a series of efficient simulation algorithmsProceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3329995.3330004(1-12)Online publication date: 20-Jun-2017
https://dl.acm.org/doi/10.5555/3329995.3330004

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