# 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}
}```
• M. Kolarz
• Published 1 October 2010
• Computer Science, Mathematics
• RAIRO Theor. Informatics Appl.
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.
8 Citations

### Domino Graphs and the Decipherability of Directed Figure Codes

A (variant of) domino graph is developed that will allow us to decide some of the decipherability kinds of directed figure codes by searching the graph for specific paths, and characterizes directed figure decipherability by graph properties.

### Decidability of multiset, set and numerically decipherable directed figure codes

This work considers decipherability of directed figure codes, where directed figures are defined as labelled polyominoes with designated start and end points, equipped with catenation operation that may use a merging function to resolve possible conflicts.

### A pr 2 01 6 Decidability of multiset , set and numerically decipherable directed figure codes

This work considers decipherability of directed figure codes, where directed figures are defined as labelled polyominoes with designated start and end points, equipped with catenation operation that may use a merging function to resolve possible conflicts.

### Testing decipherability of directed figure codes with domino graphs

• Computer Science
• 2014
A (variant of) domino graph is developed that will allow us to decide some of the decipherability kinds by searching the graph for specific paths, and characterizes directed figure decipherability by graph properties.

### Multiset, Set and Numerically Decipherable Codes over Directed Figures

• Computer Science
IWOCA
• 2012
This work considers decipherability of directed figure codes, where directed figures are defined as labelled polyominoes with designated start and end points, equipped with catenation operation that may use a merging function to resolve possible conflicts.

### Plane-Filling Properties of Directed Figures

This paper proposes a model based on directed figures with partial catenation, demonstrating a unifying approach that could be useful for the study of self-assembly and proves several undecidability results related to filling the plane with a given set of figures and formation of infinite and semiinfinite zippers.

### Combinatorial Algorithms

• S. Smyth
• Mathematics
Lecture Notes in Computer Science
• 2012
The relationships between the girth and the quasi-completeness of a graph are established and an upper bound is derived for the largest order γ-quasi-complete subgraph in a graph of minimum degree r is derived.

### Directed Figure Codes with Weak Equality

This work considers directed figures defined as labelled polyominoes with designated start and end points, equipped with catenation operation that uses a merging function to resolve possible conflicts, creating a new tool for e.g. image analysis and retrieval.