RAIRO - Theoretical Informatics and Applications

Research Article

The code problem for directed figures

Michał Kolarz

Institute of Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland; mkol@smp.if.uj.edu.pl


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.

(Received March 18 2009)

(Accepted November 5 2010)

(Online publication February 28 2011)

Key Words:

  • Directed figures;
  • variable-length codes;
  • codicity verification;
  • Sardinas-Patterson algorithm

Mathematics Subject Classification:

  • 68R15;
  • 68R99