This article is cited in 6 papers

The XV International Conference "Problems of Theoretical Cybernetics"

Clones, Co-Clones, Hyperclones and Superclones

N. A. Peryazev

Irkutsk State Pedagogical University

Abstract: Resolvability operation on set of partial hyperoperations is introduced into consideration. The superclone is defined as algebra with the basic set of partial hyperoperations and two-place operation of substitution, single operations of cyclic shift of arguments, of argument transposition, of argument identification, of resolvability and nullary operations specifying operation of designing and everywhere uncertain operation. The relation of superclones to partial hyperclones, to co-clones, and to clones is studied. The statement about isomorphism of a lattice of superclones and lattice of co-clones over identical sets is proved.

Keywords: resolvability operation, hyperoperation, clone, superclone, partial hyperoperation, partial hyperclone, co-clone, lattice.

UDC: 519.7

Received: 31.03.2009

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