Strategies to scan pictures with automata based on Wang tiles
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 45 (2011) no. 1, pp. 163-180.

Wang automata are devices for picture language recognition recently introduced by us, which characterize the class REC of recognizable picture languages. Thus, Wang automata are equivalent to tiling systems or online tessellation acceptors, and are based like Wang systems on labeled Wang tiles. The present work focus on scanning strategies, to prove that the ones Wang automata are based on are those following four kinds of movements: boustrophedonic, “L-like”, “U-like”, and spirals.

DOI : 10.1051/ita/2011016
Classification : 68Q05, 68Q10, 68Q45
Mots-clés : picture languages, 2D languages, Wang systems, 2D automata, scanning strategies 
@article{ITA_2011__45_1_163_0,
     author = {Lonati, Violetta and Pradella, Matteo},
     title = {Strategies to scan pictures with automata based on {Wang} tiles},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {163--180},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {1},
     year = {2011},
     doi = {10.1051/ita/2011016},
     mrnumber = {2776859},
     zbl = {1219.68100},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ita/2011016/}
}
TY  - JOUR
AU  - Lonati, Violetta
AU  - Pradella, Matteo
TI  - Strategies to scan pictures with automata based on Wang tiles
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2011
SP  - 163
EP  - 180
VL  - 45
IS  - 1
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/ita/2011016/
DO  - 10.1051/ita/2011016
LA  - en
ID  - ITA_2011__45_1_163_0
ER  - 
%0 Journal Article
%A Lonati, Violetta
%A Pradella, Matteo
%T Strategies to scan pictures with automata based on Wang tiles
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2011
%P 163-180
%V 45
%N 1
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/ita/2011016/
%R 10.1051/ita/2011016
%G en
%F ITA_2011__45_1_163_0
Lonati, Violetta; Pradella, Matteo. Strategies to scan pictures with automata based on Wang tiles. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 45 (2011) no. 1, pp. 163-180. doi : 10.1051/ita/2011016. http://archive.numdam.org/articles/10.1051/ita/2011016/

[1] M. Anselmo, D. Giammarresi and M. Madonia, From determinism to non-determinism in recognizable two-dimensional languages, in Proc. DLT 2007. Lecture Notes in Computer Science 4588 (2007) 36-47. | MR | Zbl

[2] M. Anselmo, D. Giammarresi and M. Madonia, Tiling automaton: A computational model for recognizable two-dimensional languages, in Proc. CIAA 2007. Lecture Notes in Computer Science 4783 (2007) 290-302. | MR | Zbl

[3] A. Bertoni, M. Goldwurm and V. Lonati, On the complexity of unary tiling-recognizable picture languages. Fundm. Inform. 91 (2009) 231-249. | MR | Zbl

[4] B. Borchert and K. Reinhardt, Deterministically and sudoku-deterministically recognizable picture languages, in Proc. LATA (2007).

[5] S. Bozapalidis and A. Grammatikopoulou, Recognizable picture series. Journal of Automata, Languages and Combinatorics 10 (2005) 159-183. | MR | Zbl

[6] R. Brijder and H.J. Hoogeboom, Perfectly quilted rectangular snake tilings. Theor. Comput. Sci. 410 (2009) 1486-1494. | MR | Zbl

[7] Y. Brun, Solving NP-complete problems in the tile assembly model. Theor. Comput. Sci. 395 (2008) 31-46. | MR | Zbl

[8] L. Cavallaro, E. Di Nitto, C.A. Furia and M. Pradella, A tile-based approach for self-assembling service compositions, in Proc. ICECCS'10. St. Anne's College, University of Oxford (2010).

[9] L. De Prophetis and S. Varricchio, Recognizability of rectangular pictures by Wang systems. Journal of Automata, Languages and Combinatorics 2 (1997) 269-288. | MR | Zbl

[10] L.W.E. Winfree, F. Liu and N. Seeman, Design and self-assembly of two-dimensional DNA crystals. Nature 394 (1998) 439-544.

[11] D. Giammarresi and A. Restivo, Recognizable picture languages. Int. J. Pattern Recogn. Artif. Intell. 6 (1992) 241-256.

[12] D. Giammarresi and A. Restivo, Two-dimensional languages, in Handbook of Formal Languages 3. A. Salomaa and G. Rozenberg, Eds. Beyond Words, Springer-Verlag, Berlin (1997) 215-267. | MR | Zbl

[13] K. Inoue and A. Nakamura, Some properties of two-dimensional on-line tessellation acceptors. Inform. Sci. 13 (1977) 95-121. | MR | Zbl

[14] K. Lindgren, C. Moore and M. Nordahl, Complexity of two-dimensional patterns. J. Statist. Phys. 91 (1998) 909-951. | MR | Zbl

[15] V. Lonati and M. Pradella, Deterministic recognizability of picture languages with Wang automata. Discrete Mathematics and Theoretical Computer Science (to appear). | MR | Zbl

[16] V. Lonati and M. Pradella, Snake-deterministic tiling systems, in Proc. MFCS 2009. Lecture Notes in Computer Science 5734 (2009) 549-560. | MR | Zbl

[17] V. Lonati and M. Pradella, Picture recognizability with automata based on Wang tiles, in Proc. SOFSEM 2010. Lecture Notes in Computer Science 5901 (2010) 576-587. | Zbl

[18] M. Pradella, A. Morzenti and P. San Pietro, The symmetry of the past and of the future: Bi-infinite time in the verification of temporal properties, in Proc. of 6th joint meeting of ESEC/FSE. Dubrovnik, Croatia (2007).

[19] H. Wang, Proving theorems by pattern recognition II. Bell Systems Technical Journal 40 (1961) 1-42.

Cité par Sources :