Abstract
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.
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Salehi, S. (2003). A Completeness Property of Wilke’s Tree Algebras. In: Rovan, B., Vojtáš, P. (eds) Mathematical Foundations of Computer Science 2003. MFCS 2003. Lecture Notes in Computer Science, vol 2747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45138-9_60
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DOI: https://doi.org/10.1007/978-3-540-45138-9_60
Publisher Name: Springer, Berlin, Heidelberg
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