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Siberian Mathematical Journal

, Volume 60, Issue 3, pp 497–507 | Cite as

The Partial Clone of Linear Tree Languages

  • N. Lekkoksung
  • K. DeneckeEmail author
Article
  • 12 Downloads

Abstract

A term, also called a tree, is said to be linear, if each variable occurs in the term only once. The linear terms and sets of linear terms, the so-called linear tree languages, play some role in automata theory and in the theory of formal languages in connection with recognizability. We define a partial superposition operation on sets of linear trees of a given type τ and study the properties of some many-sorted partial clones that have sets of linear trees as elements and partial superposition operations as fundamental operations. The endomorphisms of those algebras correspond to nondeterministic linear hypersubstitutions.

Keywords

linear term linear tree language clone partial clone linear hypersubstitution nondeterministic linear hypersubstitution 

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References

  1. 1.
    Lawvere F. W., Functorial Semantics of Algebraic Theories, Thes. Doct. Philosophy, Columbia Univ., New York (1963).CrossRefzbMATHGoogle Scholar
  2. 2.
    Denecke K., “The partial clone of linear terms,” Sib. Math. J., vol. 57, no. 4, 589–598 (2016).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Denecke K., Glubudom P., and Koppitz J., “Power clones and non-deterministic hypersubstitutions,” Asian-Eur. J. Math., vol. 1, no. 2, 177–188 (2008).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Lekkoksung N. and Jampachon P., “Non-deterministic linear hypersubstitutions,” Discuss. Math. Gen. Algebra Appl., vol. 35, 97–103 (2015).MathSciNetCrossRefGoogle Scholar
  5. 5.
    Glubudom P., Clones of Tree Languages and Non-Deterministic Hypersubstitutions, Thesis for Doctoral, Univ. Potsdam (2008).zbMATHGoogle Scholar
  6. 6.
    Rabin M. O. and Scott D., “Finite automata and their decision problems,” IBM J. Res. Develop., vol. 3, no. 2, 114–125 (1959).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Sarasit N., Algebraic Properties of Sets of Terms, Thesis for Doctoral, Univ. Potsdam (2011).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.University of Potsdam, Institute of MathematicsPotsdamGermany
  2. 2.KhonKaen University, Department of MathematicsKhonKaenThailand

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