Input Products for Weighted Extended Top-Down Tree Transducers

  • Andreas Maletti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6224)


A weighted tree transformation is a function \(\tau \colon T_\Sigma \times T_\Delta \to A\) where T Σ and T Δ are the sets of trees over the ranked alphabets Σ and Δ, respectively, and A is the domain of a semiring. The input and output product of τ with tree series \(\varphi \colon T_\Sigma \to A\) and \(\psi \colon T_\Delta \to A\) are the weighted tree transformations \(\varphi \triangleleft \tau\) and \(\tau \triangleright \psi\), respectively, which are defined by \((\varphi \triangleleft \tau)(t, u) = \varphi(t) \cdot \tau(t, u)\) and \((\tau \triangleright \psi)(t, u) = \tau(t, u) \cdot \psi(u)\) for every t ∈ T Σ and u ∈ T Δ. In this contribution, input and output products of weighted tree transformations computed by weighted extended top-down tree transducers (wxtt) with recognizable tree series are considered. The classical approach is presented and used to solve the simple cases. It is shown that input products can be computed in three successively more difficult scenarios: nondeleting wxtt, wxtt over idempotent semirings, and weighted top-down tree transducers over rings.


Output Product Tree Series Weighted Tree Input Product Input Tree 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Andreas Maletti
    • 1
  1. 1.Departament de Filologies RomàniquesUniversitat Rovira i VirgiliTarragonaSpain

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