L Systems pp 162-176 | Cite as

Free groups in Lindenmayer systems

  • Peter Johansen
  • Erik Meiling
New Attacks On Dol Equivalence Problem
Part of the Lecture Notes in Computer Science book series (LNCS, volume 15)


Locally catenative equations are defined in the free group. It is shown that if the free group generated by a DOL sequence is finitely generated then there exists a locally catenative equation in the free group which defines the DOL sequence. An algorithm is given which finds the generators of the free group if it is finitely generated.

A conjecture is stated in terms of the existence of a certain group. The conjecture implies the solvability of the DOL equivalence problem.


Free Group Equivalence Group Recurrence Equation Equivalence Problem Free Generator 


  1. 1.
    Peter Johansen, An Algebraic Normal Form for Regular Events, Polyteknisk Forlag, Lyngby 1972.Google Scholar
  2. 2.
    J.Clausen, J.Hammerum, E.Meiling, T.Skovgaard, Automata Theory in Free Groups, manuscript to be submitted to Acta Informatica..Google Scholar
  3. 3.
    M. Hall. The Theory of Groups, The Macmillan Company, New York, 1959.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • Peter Johansen
    • 1
  • Erik Meiling
    • 1
  1. 1.Datalogisk institutKøbenhavns UniversitetThe Netherlands

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