Strategies to scan pictures with automata based on Wang tiles

Violetta Lonati; Matteo Pradella

RAIRO - Theoretical Informatics and Applications (2011)

  • Volume: 45, Issue: 1, page 163-180
  • ISSN: 0988-3754

Abstract

top
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.

How to cite

top

Lonati, Violetta, and Pradella, Matteo. "Strategies to scan pictures with automata based on Wang tiles." RAIRO - Theoretical Informatics and Applications 45.1 (2011): 163-180. <http://eudml.org/doc/222010>.

@article{Lonati2011,
abstract = { 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. },
author = {Lonati, Violetta, Pradella, Matteo},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Picture languages; 2D languages; Wang systems; 2D automata; scanning strategies; picture languages},
language = {eng},
month = {3},
number = {1},
pages = {163-180},
publisher = {EDP Sciences},
title = {Strategies to scan pictures with automata based on Wang tiles},
url = {http://eudml.org/doc/222010},
volume = {45},
year = {2011},
}

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
DA - 2011/3//
PB - EDP Sciences
VL - 45
IS - 1
SP - 163
EP - 180
AB - 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.
LA - eng
KW - Picture languages; 2D languages; Wang systems; 2D automata; scanning strategies; picture languages
UR - http://eudml.org/doc/222010
ER -

References

top
  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 Science4588 (2007) 36–47.  Zbl1202.68218
  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 Science4783 (2007) 290–302.  Zbl1139.68353
  3. A. Bertoni, M. Goldwurm and V. Lonati, On the complexity of unary tiling-recognizable picture languages. Fundm. Inform.91 (2009) 231–249.  Zbl1179.68067
  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 Combinatorics10 (2005) 159–183.  Zbl1161.68514
  6. R. Brijder and H.J. Hoogeboom, Perfectly quilted rectangular snake tilings. Theor. Comput. Sci.410 (2009) 1486–1494.  Zbl1162.68021
  7. Y. Brun, Solving NP-complete problems in the tile assembly model. Theor. Comput. Sci.395 (2008) 31–46.  Zbl1145.68018
  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 Combinatorics2 (1997) 269–288.  Zbl0908.68109
  10. L.W.E. Winfree, F. Liu and N. Seeman, Design and self-assembly of two-dimensional DNA crystals. Nature394 (1998) 439–544.  
  11. D. Giammarresi and A. Restivo, Recognizable picture languages. Int. J. Pattern Recogn. Artif. Intell.6 (1992) 241–256.  Zbl1217.68129
  12. D. Giammarresi and A. Restivo, Two-dimensional languages, in Handbook of Formal Languages3. A. Salomaa and G. Rozenberg, Eds. Beyond Words, Springer-Verlag, Berlin (1997) 215–267.  
  13. K. Inoue and A. Nakamura, Some properties of two-dimensional on-line tessellation acceptors. Inform. Sci.13 (1977) 95–121.  Zbl0371.94067
  14. K. Lindgren, C. Moore and M. Nordahl, Complexity of two-dimensional patterns. J. Statist. Phys.91 (1998) 909–951.  Zbl0917.68156
  15. V. Lonati and M. Pradella, Deterministic recognizability of picture languages with Wang automata. Discrete Mathematics and Theoretical Computer Science (to appear).  Zbl1286.68291
  16. V. Lonati and M. Pradella, Snake-deterministic tiling systems, in Proc. MFCS 2009. Lecture Notes in Computer Science5734 (2009) 549–560.  Zbl1250.68168
  17. V. Lonati and M. Pradella, Picture recognizability with automata based on Wang tiles, in Proc. SOFSEM 2010. Lecture Notes in Computer Science5901 (2010) 576–587.  Zbl1274.68160
  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 Journal40 (1961) 1–42.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.