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.
@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}, volume = {44}, year = {2010}, pages = {489-506}, doi = {10.1051/ita/2011005}, mrnumber = {2775408}, language = {en}, url = {http://dml.mathdoc.fr/item/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) pp. 489-506. doi : 10.1051/ita/2011005. http://gdmltest.u-ga.fr/item/ITA_2010__44_4_489_0/
[1] Polyomino tilings, cellular automata and codicity. Theoret. Comput. Sci. 147 (1995) 165-180. | Zbl 0873.68139
and ,[2] A codicity undecidable problem in the plane. Theoret. Comput. Sci. 303 (2003) 417-430. | Zbl 1053.68067
and ,[3] Theory of Codes. Academic Press (1985). | Zbl 0587.68066
and ,[4] Adding symbolic information to picture models: definitions and properties. Theoret. Comput. Sci. 337 (2005) 51-104. | Zbl 1077.68041
, and ,[5] Directed figure codes are decidable. Discrete Mathematics and Theoretical Computer Science 11 (2009) 1-14. | Zbl 1193.68155
and ,[6] Codes and equations on trees. Theoret. Comput. Sci. 255 (2001) 483-509. | Zbl 0974.68095
and ,[7] Defect theorem in the plane. RAIRO-Theor. Inf. Appl. 41 (2007) 403-409. | Zbl 1144.68048
,[8] 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 1094.68051
and ,[9] Some open problems in decidability of brick (labelled polyomino) codes, in Cocoon 2004 Proceedings. Lect. Notes Comput. Sci. 3106 (2004) 72-81. | Zbl 1091.05016
and ,