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Mathematical systems theory

, Volume 27, Issue 2, pp 159–181 | Cite as

Semantics of trees

  • A. Ehrenfeucht
  • G. Rozenberg
  • K. Salomaa
Article
  • 30 Downloads

Abstract

We introduce F-structures and investigate interpretations of trees in F-structures. Thus trees are viewed as schemes of computations in F-structures. Every tree is shown to be strongly equivalent to some chain-free tree. This enables us to use the grammatical codings of [2] to define formulas for arbitrary interpreted trees. We also introduce a syntactic way to compute the values of interpreted trees.

Keywords

Computational Mathematic Grammatical Codings 
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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References

  1. [1]
    A. Ehrenfeucht and G. Rozenberg, On basic properties of DOS systems and languages,Inform. and Control,47 (1980), 137–153.Google Scholar
  2. [2]
    A. Ehrenfeucht and G. Rozenberg, Grammatical codes of trees,Discrete Appl. Math.,32 (1991), 103–129.Google Scholar
  3. [3]
    A. Ehrenfeucht, P. ten Pas, and G. Rozenberg, Properties of grammatical codes of trees, Tech. Report No. RUL-91-07, Department of Computer Science, University of Leiden, 1991. To appear inTheoretical Computer Science.Google Scholar
  4. [4]
    H. C. M. Kleijn and G. Rozenberg, Context-free like restrictions on selective rewriting,Theoret. Comput. Sci.,16 (1981), 237–269.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1994

Authors and Affiliations

  • A. Ehrenfeucht
    • 1
  • G. Rozenberg
    • 2
    • 1
  • K. Salomaa
    • 3
  1. 1.Department of Computer ScienceUniversity of Colorado at BoulderBoulderUSA
  2. 2.Department of Computer ScienceLeiden UniversityRA LeidenThe Netherlands
  3. 3.Department of MathematicsUniversity of TurkuTurkuFinland

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