A Completeness Property of Wilke’s Tree Algebras

  • Saeed Salehi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2747)


Wilke’s tree algebra formalism for characterizing families of tree languages is based on six operations involving letters, binary trees and binary contexts. In this paper a completeness property of these operations is studied. It is claimed that all functions involving letters, binary trees and binary contexts which preserve all syntactic tree algebra congruence relations of tree languages are generated by Wilke’s functions, if the alphabet contains at least seven letters. The long proof is omitted due to page limit. Instead, a corresponding theorem for term algebras, which yields a special case of the above mentioned theorem, is proved: in every term algebra whose signature contains at least seven constant symbols, all congruence preserving functions are term functions.


Binary Tree Universal Algebra Congruence Relation Term Function Constant Symbol 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Saeed Salehi
    • 1
  1. 1.Turku Center for Computer ScienceTurkuFIN

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