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International Workshop on Graph Grammars and Their Application to Computer Science

Graph Grammars 1978: Graph-Grammars and Their Application to Computer Science and Biology pp 367–378Cite as

Complexity of pattern generation by map-L systems

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 73))

Abstract

There are additional results which can be proved such as the following:

Theorem 7.1:

Theorem 7.2: For every m there is no such that for any n⩾no there is ko(m,n) such that c nm , c n+km are incomparable but not disjoint for k⩾ko(m,n).

Conjecture: ko(m,n)≡1.

One can summarize the results exhibited in this paper in the following two-dimensional infinite diagram:

The symbol " → " stand for inclusion relation and strict inclusion or equality appear according to the theorems in this paper.

This work is based on the D.Sc. research of the second author under the supervision of the first.

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Bibliography

  1. Carlyle, J.W., Greibach, S.A., Paz, A., "A Two-Dimensional Generating System Modelling Growth by Binary Cell Division", IEEE 15th Annual Symposium on Switching and Automata Theory, October 1974, 1–12.

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Author information

Authors and Affiliations

  1. Computer Science Department Technion, Israel Institute of Technology, Haifa, Israel

    A. Paz & Y. Raz

Authors
  1. A. Paz
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  2. Y. Raz
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Volker Claus Hartmut Ehrig Grzegorz Rozenberg

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© 1979 Springer-Verlag Berlin Heidelberg

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Paz, A., Raz, Y. (1979). Complexity of pattern generation by map-L systems. In: Claus, V., Ehrig, H., Rozenberg, G. (eds) Graph-Grammars and Their Application to Computer Science and Biology. Graph Grammars 1978. Lecture Notes in Computer Science, vol 73. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0025733

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  • DOI: https://doi.org/10.1007/BFb0025733

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09525-5

  • Online ISBN: 978-3-540-35091-0

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