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Semirigid sets of quasilinear clones

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4 Author(s)
Nozaki, A. ; Int. Christian Univ., Tokyo, Japan ; Pogosyan, G. ; Miyakawa, M. ; Rosenberg, I.G.

Let k be a prime and G a Galois field on k :={0,1,. . .,k-1}. The set of all quasilinear (or affine with respect to G) k-valued logic functions is a maximal clone called quasilinear. A family of quasilinear clones on k is semirigid if the clones of the family share exactly the constant functions and the projections. Semirigid sets of quasilinear clones are needed for the classification of bases of k-valued logic, which is unknown for k>3. The authors characterize all semirigid sets of quasilinear clones. In particular, for k=5 they describe all semirigid triples of quasilinear clones and show that no such pair exists. For every prime k>5 they exhibit a semirigid pair of quasi-linear clones. The techniques used are based on elementary number theory and on polynomials over G

Published in:

Multiple-Valued Logic, 1993., Proceedings of The Twenty-Third International Symposium on

Date of Conference:

24-27 May 1993

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