Nd-hypersubstitutions of many-sorted algebras

• Autorzy: Denecke K. , Lekkoksung S.
• Języki publikacji: EN

Abstrakty

EN

A non-deterministic hypersubstitution maps any operation symbol of type ? to a tree language. Non-deterministic hypersubstitutions can be extended to mappings which map tree languages to tree languages preserving the arities ([2]). We can extend those hypersubstitutions to many-sorted non-deterministic hypersubstitutions which map any operation symbol to a tree language of the corresponding sort ([5]). The aim of this paper is to show that the extension of a many-sorted non-deterministic hyper-substitution is an endomorphism of some clone and that the set of all non-deterministic hypersubstitutions of each sort forms a semigroup. These results can be applied to study M-solid many-sorted varieties of tree languages (see [4]).

Słowa kluczowe

EN

many-sorted algebras; non-deterministic hypersubstitutions; many-sorted tree language

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2010
• Tom: Vol. 43, nr 3
• Strony: 519--537
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Denecke K.

autor

Lekkoksung S.

• Universität Potsdam Institute of Mathematics Am Neuen Palais P.U.M.A. 14415 Potsdam, Germany,

Bibliografia

• [1] K. Denecke, S. Lekkoksung, Hypersubstitutions of many-sorted algebras, Asian-European J. Math. I 3 (2008), 337–346.
• [2] K. Denecke, P. Glubudom, Nd-solid varieties, Discuss. Math., General Algebra and Applications 27 (2007), 245–262.
• [3] E. Graczyńska, D. Schweigert, Hypervarieties of a given type, Algebra Universalis, 27 (1990), 305–318.
• [4] S. Salehi, Varieties of Tree Languages, TUCS Dissertations, No. 64, July 2005.
• [5] S. Salehi, M. Steinby, Varieties of Many-Sorted Recognizable Sets, PU.M.A. Vol. 18 (2007), No. 3–4, 319–343.