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Finite tree automata with cost functions

  • Helmut Seidl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 581)

Abstract

Cost functions for tree automata are mappings from transitions to (tuples of) polynomials over some semiring. We consider four semirings, namely N the semiring of nonnegative integers, A the “arctical semiring”, T the tropical semiring and F the semiring of finite subsets of nonnegative integers. We show: for semirings N and A it is decidable in polynomial time whether or not the costs of accepting computations is bounded; for F it is decidable in polynomial time whether or not the cardinality of occurring cost sets is bounded. In all three cases we derive explicit upper bounds. For semiring T we are able to derive similar results at least in case of polynomials of degree at most 1.

For N and A we extend our results to multi-dimensional cost functions.

Keywords

Cost Function Polynomial Time Strong Component Tree Automaton Tree Language 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Helmut Seidl
    • 1
  1. 1.Fachbereich InformatikUniversität des Saarlandes Im StadtwaldGermany

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