Mathematical systems theory

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

Semantics of trees

  • A. Ehrenfeucht
  • G. Rozenberg
  • K. Salomaa


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.


Computational Mathematic Grammatical Codings 
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  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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