The code problem for directed figures
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 4, pp. 489-506.

We consider directed figures defined as labelled polyominoes with designated start and end points, with two types of catenation operations. We are especially interested in codicity verification for sets of figures, and we show that depending on the catenation type the question whether a given set of directed figures is a code is decidable or not. In the former case we give a constructive proof which leads to a straightforward algorithm.

DOI : 10.1051/ita/2011005
Classification : 68R15, 68R99
Mots-clés : directed figures, variable-length codes, codicity verification, Sardinas-Patterson algorithm 
@article{ITA_2010__44_4_489_0,
     author = {Kolarz, Micha{\l}},
     title = {The code problem for directed figures},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {489--506},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {4},
     year = {2010},
     doi = {10.1051/ita/2011005},
     mrnumber = {2775408},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ita/2011005/}
}
TY  - JOUR
AU  - Kolarz, Michał
TI  - The code problem for directed figures
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2010
SP  - 489
EP  - 506
VL  - 44
IS  - 4
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/ita/2011005/
DO  - 10.1051/ita/2011005
LA  - en
ID  - ITA_2010__44_4_489_0
ER  - 
%0 Journal Article
%A Kolarz, Michał
%T The code problem for directed figures
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2010
%P 489-506
%V 44
%N 4
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/ita/2011005/
%R 10.1051/ita/2011005
%G en
%F ITA_2010__44_4_489_0
Kolarz, Michał. The code problem for directed figures. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 4, pp. 489-506. doi : 10.1051/ita/2011005. http://archive.numdam.org/articles/10.1051/ita/2011005/

[1] P. Aigrain and D. Beauquier, Polyomino tilings, cellular automata and codicity. Theoret. Comput. Sci. 147 (1995) 165-180. | Zbl

[2] D. Beauquier and M. Nivat, A codicity undecidable problem in the plane. Theoret. Comput. Sci. 303 (2003) 417-430. | Zbl

[3] J. Berstel and D. Perrin, Theory of Codes. Academic Press (1985). | Zbl

[4] G. Costagliola, F. Ferrucci and C. Gravino, Adding symbolic information to picture models: definitions and properties. Theoret. Comput. Sci. 337 (2005) 51-104. | Zbl

[5] M. Kolarz and W. Moczurad, Directed figure codes are decidable. Discrete Mathematics and Theoretical Computer Science 11 (2009) 1-14. | Zbl

[6] S. Mantaci and A. Restivo, Codes and equations on trees. Theoret. Comput. Sci. 255 (2001) 483-509. | Zbl

[7] W. Moczurad, Defect theorem in the plane. RAIRO-Theor. Inf. Appl. 41 (2007) 403-409. | Zbl

[8] M. Moczurad and W. Moczurad, Decidability of simple brick codes, in Mathematics and Computer Science, Vol. III (Algorithms, Trees, Combinatorics and Probabilities). Trends in Mathematics, Birkhäuser (2004), 541-542. | Zbl

[9] M. Moczurad and W. Moczurad, Some open problems in decidability of brick (labelled polyomino) codes, in Cocoon 2004 Proceedings. Lect. Notes Comput. Sci. 3106 (2004) 72-81. | Zbl

Cité par Sources :