Equational weighted tree transformations with discounting

  • Authors:

  • Zoltán Fülöp;George Rahonis

  • Affiliations:

  • Department of Computer Science, University of Szeged, Szeged, Hungary;-

  • Venue:
  • Algebraic Foundations in Computer Science
  • Year:
  • 2011

Quantified Score

Hi-index 0.00

Visualization

Abstract

We consider systems of equations of polynomial weighted tree transformations over the max-plus (or: arctic) semiring ℝ max =( ℝ +∪{−∞}, max ,+,−∞,0). We apply discounting with a parameter 0≤dd-solution, of such systems. We compute least d-solutions under u-substitution mode, where u=[IO] or u=OI. We define a weighted relation over ℝ max to be u-d-equational, if it is a component of the least u-d-solution of such a system of equations in a pair of algebras. We mainly focus on u-d-equational weighted tree transformations which are equational relations obtained by considering the least u-d-solutions in pairs of term algebras. We also introduce u-d-equational weighted tree languages over ℝ max . We characterize u-d-equational weighted tree transformations in terms of weighted tree transformations defined by weighted d-bimorphisms, which are bimorphisms from d-recognizable weighted tree languages. Finally, we prove that a weighted relation is u-d-equational if and only if it is, roughly speaking, the morphic image of a weighted u-d-equational tree transformation.