Finite tree automata with cost functions

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


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.


Cost Function Polynomial Time Strong Component Tree Automaton Tree Language 
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  1. [CouMo90]
    B. Courcelle, M. Mosbah: Monadic second-order evaluations on treedecomposable graphs. Tech. Report LaBRI No. 90-110, Bordeaux, 1990Google Scholar
  2. [GeSt84]
    F. Gecseg, M. Steinby: Tree automata. Akademiai Kiado, Budapest, 1984Google Scholar
  3. [GiSch88]
    R. Giegerich, K. Schmal: Code selection techniques: pattern matching, tree parsing and inversion of derivors. Proc. of ESOP 1988, LNCS 300 pp. 245–268Google Scholar
  4. [HaKre89]
    A. Habel, H.-J. Kreowski, W. Vogler: Decidable boundedness problems for hyperedge-replacement grammars. Proc. TAPSOFT '89 vol. 1, LNCS 352, pp. 275–289; long version to appear in TCSGoogle Scholar
  5. [MöWi82]
    U. Möncke, R. Wilhelm: Iterative algorithms on grammar graphs. Proc. 8th Conf. on Graphtheoretic Concepts in Computer Science, Hanser Verlag 1982, pp. 177–194Google Scholar
  6. [Paul78]
    W. Paul: Komplexitätstheorie. B.G. Teubner Verlag Stuttgart 1978Google Scholar
  7. [Sei89]
    H. Seidl: On the finite degree of ambiguity of finite tree automata. Acta Inf. 26, pp. 527–542 (1989)Google Scholar
  8. [Sei90]
    H. Seidl: Single-valuedness of tree transducers is decidable in polynomial time. To appear in: TCS, special issue of CAAP 90Google Scholar
  9. [Sei91]
    H. Seidl: Ambiguity and Valuedness. To appear in: M. Nivat, A. Podelski (eds.): “Definability and Recognizability of Sets of Trees”. Elsevier AmsterdamGoogle Scholar
  10. [WeiWi88]
    Two tree pattern matchers for code selection. Proc. 2nd CCHSC Workshop 1988, LNCS 371, pp. 215–229Google Scholar

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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