# The code problem for directed figures

@article{Kolarz2010TheCP, title={The code problem for directed figures}, author={Michal Kolarz}, journal={RAIRO Theor. Informatics Appl.}, year={2010}, volume={44}, pages={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.

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## References

SHOWING 1-10 OF 10 REFERENCES

### Directed figure codes are decidable

- Computer ScienceDiscret. Math. Theor. Comput. Sci.
- 2009

It is proved that in this setting verification whether a given finite set of directed Figures is a code is decidable and a constructive algorithm is given and the status of the defect effect for directed figures is clarified.

### Decidability of Simple Brick Codes

- Mathematics
- 2004

Bricks are polyominoes with labelled cells. The problem whether a given set of bricks is a code,is undecidable in general. It is open for two-element sets. Here we consider sets consisting of square…

### Some Open Problems in Decidability of Brick (Labelled Polyomino) Codes

- Mathematics, Computer ScienceCOCOON
- 2004

The codicity problem is decidable for sets with keys of size n when n = 1 and, under obvious constraints, for every n, and it is proved that it is undecidable in the general case of sets with Key n, when n≥ 6.

### Defect theorem in the plane

- MathematicsRAIRO Theor. Informatics Appl.
- 2007

This work establishes the defect property in the case of three dominoes ( n × 1 or 1 × n rectangles) in the context of labelled polyominoes, i.e. two-dimensional figures.

### Adding symbolic information to picture models: definitions and properties

- Computer ScienceTheor. Comput. Sci.
- 2005

### Polyomino tilings

- cellular automata and codicity. Theoret. Comput. Sci. 147
- 1995