L Systems pp 78-92 | Cite as

On the size of dol languages

  • Paul M. B. Vitányi
Towards Characterization Results
Part of the Lecture Notes in Computer Science book series (LNCS, volume 15)


Languages generated by monogenic (i.e. deterministic) context independent Lindenmayer systems (DOL systems) are investigated. Necessary and sufficient conditions are established under which the language generated by a DOL system is finite. Thus, sharp bounds on the cardinality of such a language are obtained. A feasible solution for the membership problem is given. The problems are solved of what is the minimum sized alphabet over which there is a DOL language of cardinality n and, conversely, what is the maximum sized finite DOL language over an alphabet of m letters. This in turn provides us with some number theoretic functions, interesting in their own right, of which several properties, interrelations and asymptotic approximations are derived.


Decision Procedure Asymptotic Approximation Chinese Remainder Theorem Membership Problem Formal Language Theory 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • Paul M. B. Vitányi
    • 1
  1. 1.Mathematisch CentrumAmsterdamThe Netherlands

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