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Ternary Cyclo-Decompositions
December 1968 (vol. 17 no. 12)
pp. 1175-1176
Abstract?This note discusses a particular kind of ternary functional decomposition based on a ternary function ? to be performed on the set of composite functions. Such function is closely related to the cycling concept of Postian algebras. A systematic method is given to determine the set of all decompositions of that kind admitted by the function. Such set is called the cyclo-set and it is proved that it is a filter in the partitions lattice. Since any partition of the lattice can be expressed as an intersection of cardinality-2 partitions, it follows that the method consists merely in finding the infimum of the cardinality-2 partitions belonging to the cyclo-set and then determining the filter having this infimum as vertex. The existence of proper subsets of the cardinality-2 partitions set leading to the determination of the ifiter-vertex is discussed, and results obtained for functions of domain-order up to seven are stated. Finally, the total number of cyclo-decompositions for a given partitional structure is calculated.
Index Terms:
Index Terms?Decompositions, filter, lattice, partition, ternary.
Citation:
H. Arango, J. Santos, A. Chacur, "Ternary Cyclo-Decompositions," IEEE Transactions on Computers, vol. 17, no. 12, pp. 1175-1176, Dec. 1968, doi:10.1109/TC.1968.226884
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