Reference : Minimal coverings of maximal partial clones
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Minimal coverings of maximal partial clones
Schölzel, Karsten mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Proceedings of The International Symposium on Multiple-Valued Logic
39th International Symposium on Multiple-Valued Logic, ISMVL 2009
21 May 2009 through 23 May 2009
Naha, Okinawa
[en] Partial clones ; Partial functions ; Sheffer function ; Cloning ; Many valued logics
[en] A partial function f on a κ-element set Eκ is a partial Sheffer function if every partial function on Eκ is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone on Eκ, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on Eκ. We show that for each κ ≥ 3 there exists a unique minimal covering.
Graduate School of Information Sciences of Tohoku University;IEEE Computer Society;Japan MVL Research Group

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