Questions of decidability for context-free chain code picture languages

  • Friedheld Hinz
Chapter 1 Languages
Part of the Lecture Notes in Computer Science book series (LNCS, volume 381)


A picture description is a word over the alphabet {u,d,r,l,↑↓} with the following interpretation: "move one unit line up (down, right, left, resp.) from the current point" for letter u (d,r,l, resp.) and "lift (sink) the pen" for ↑ (↓). The set of unit lines traversed with sunk pen is the picture described. A set of pictures given by a set of picture descriptions generated by a context-free grammar is called a context-free (chain code) picture language.

We show that the membership problem and the superpicture problem are undecidable for context-free and for linear context-free picture languages, while the subpicture problem is decidable. This result is in contrast to the situation for regular picture languages and for context-free picture languages generated without using a "lift the pen"-symbol. For these classes all three problems are known to be decidable, and the subpicture problem is harder than the superpicture problem (NP-complete instead of polynomial time).


Turing Machine Final Rule Chain Code Membership Problem Unit Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Friedheld Hinz
    • 1
  1. 1.RWTH Aachen, Lehrstuhl für Informatik IIAachenFRG

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