The code problem for directed figures

Michał Kolarz

RAIRO - Theoretical Informatics and Applications (2011)

  • Volume: 44, Issue: 4, page 489-506
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Kolarz, Michał. "The code problem for directed figures." RAIRO - Theoretical Informatics and Applications 44.4 (2011): 489-506. <http://eudml.org/doc/193072>.

@article{Kolarz2011,
abstract = { 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. },
author = {Kolarz, Michał},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Directed figures; variable-length codes; codicity verification; Sardinas-Patterson algorithm; directed figures},
language = {eng},
month = {2},
number = {4},
pages = {489-506},
publisher = {EDP Sciences},
title = {The code problem for directed figures},
url = {http://eudml.org/doc/193072},
volume = {44},
year = {2011},
}

TY - JOUR
AU - Kolarz, Michał
TI - The code problem for directed figures
JO - RAIRO - Theoretical Informatics and Applications
DA - 2011/2//
PB - EDP Sciences
VL - 44
IS - 4
SP - 489
EP - 506
AB - 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.
LA - eng
KW - Directed figures; variable-length codes; codicity verification; Sardinas-Patterson algorithm; directed figures
UR - http://eudml.org/doc/193072
ER -

References

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  2. D. Beauquier and M. Nivat, A codicity undecidable problem in the plane. Theoret. Comput. Sci.303 (2003) 417–430.  Zbl1053.68067
  3. J. Berstel and D. Perrin, Theory of Codes. Academic Press (1985).  Zbl0587.68066
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  5. M. Kolarz and W. Moczurad, Directed figure codes are decidable. Discrete Mathematics and Theoretical Computer Science11 (2009) 1–14.  Zbl1193.68155
  6. S. Mantaci and A. Restivo, Codes and equations on trees. Theoret. Comput. Sci.255 (2001) 483–509.  Zbl0974.68095
  7. W. Moczurad, Defect theorem in the plane. RAIRO-Theor. Inf. Appl.41 (2007) 403–409.  Zbl1144.68048
  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.  Zbl1094.68051
  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.  Zbl1091.05016

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