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Handbook of Weighted Automata pp 291–311Cite as

Lindenmayer Systems

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Abstract

The theory of Lindenmayer systems studies free monoid morphisms, free monoid substitutions and their iterations. In this chapter, we discuss similar ideas in a more general framework. Instead of a free monoid, we consider the free semi-algebra S〈Σ*〉 consisting of polynomials with non-commuting variables in Σ and coefficients in a semiring S and we study the iteration of endomorphisms of S〈Σ*〉. We allow various modes of iteration and we consider various classes of morphisms. Classical L systems are obtained as special cases by taking S to be the Boolean semiring. Our approach also generalizes the theory of algebraic series in noncommuting variables.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Turku, 20014, Turku, Finland

    Juha Honkala

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  1. Juha Honkala
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Correspondence to Juha Honkala .

Editor information

Editors and Affiliations

  1. Inst. Informatik, Universität Leipzig, Augustusplatz 10-11, Leipzig, 04109, Germany

    Manfred Droste

  2. Institut für Diskrete, TU Wien, Wiedner Hauptstr. 8-10, Wien, 1040, Austria

    Werner Kuich

  3. Fak. Informatik, TU Dresden, Nöthnitzer Str. 46, Dresden, 01187, Germany

    Heiko Vogler

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Honkala, J. (2009). Lindenmayer Systems. In: Droste, M., Kuich, W., Vogler, H. (eds) Handbook of Weighted Automata. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01492-5_8

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  • DOI: https://doi.org/10.1007/978-3-642-01492-5_8

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  • Print ISBN: 978-3-642-01491-8

  • Online ISBN: 978-3-642-01492-5

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