Title :
Polynomials as Generators of Minimal Clones
Author :
Machida, Hajime ; Pinsker, Michael
Author_Institution :
Dept. of Math., Hitotsubashi Univ., Kunitachi
Abstract :
A minimal clone is an atom of the lattice of clones. A minimal function is a function which generates a minimal clone. We consider the base set with k elements, for a prime k, as a finite field and treat functions as polynomials. Starting from binary minimal functions over GF(3), we generalize some of them and obtain binary minimal functions, as polynomials, over GF(k) for any prime k ges 3.
Keywords :
Galois fields; polynomials; Galois fields; minimal clones; minimal function; polynomials; Algebra; Boolean functions; Character generation; Cloning; Galois fields; Lattices; Logic; Mathematics; Polynomials; Power generation; Clone; Galois field; minimal clone;
Conference_Titel :
Multiple-Valued Logic, 2007. ISMVL 2007. 37th International Symposium on
Conference_Location :
Oslo
Print_ISBN :
0-7695-2831-7
DOI :
10.1109/ISMVL.2007.41
