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Equational weighted tree transformations

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Abstract

We consider systems of equations of weighted tree transformations with finite support over continuous and commutative semirings. We define a weighted relation to be equational, if it is a component of the least solution of such a system of equations in a pair of algebras. In particular, we focus on equational weighted tree transformations which are equational relations obtained by considering the least solutions of such systems in pairs of term algebras. We characterize equational weighted tree transformations in terms of weighted tree transformations defined by different weighted bimorphisms. To demonstrate the robustness of equational weighted tree transformations, we give an equational definition of the class of linear and nondeleting weighted top-down tree transformations and of the class of linear and nondeleting weighted extended top-down tree transformations. Finally, we prove that a weighted relation is equational if and only if it is, roughly speaking, the morphic image of a weighted equational tree transformation.

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Authors and Affiliations

  1. Department of Mathematics, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    Symeon Bozapalidis & George Rahonis

  2. Department of Computer Science, University of Szeged, Árpád tér 2., 6720, Szeged, Hungary

    Zoltán Fülöp

Authors
  1. Symeon Bozapalidis
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  2. Zoltán Fülöp
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  3. George Rahonis
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Corresponding author

Correspondence to Zoltán Fülöp.

Additional information

Research of the second author was supported by the TÁMOP-4.2.1/B-09/1/KONV-2010-0005 program of the Hungarian National Development Agency and the third author by the RISC-Linz Transnational Access Program, project SCIEnce (Contract No. 026133) of the European Commission FP6 for Integrated Infrastructures Initiatives.

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Bozapalidis, S., Fülöp, Z. & Rahonis, G. Equational weighted tree transformations. Acta Informatica 49, 29–52 (2012). https://doi.org/10.1007/s00236-011-0148-5

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