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Proceedings 1999 29th IEEE International Symposium on Multiple-Valued Logic (Cat. No.99CB36329) (1999)
Freiburg im Breisgau, Germany
May 20, 1999 to May 22, 1999
ISSN: 0195-623X
ISBN: 0-7695-0161-3
pp: 208
Alioune Ngom , Lakehead University
Ivan Stojmenovic , University of Ottawa
Jovisa Zunic , University of Novi Sad
ABSTRACT
We introduce the concept of multilinear partition of a point set V subset Rn and the concept of multilinear separability of a function f: V mapsto K = {0, \1dot, k-1\} Based on well- known relationships between linear partitions and minimal pairs, we derive formulae for the number of multilinear partitions of a point set in general position and of the set K2. The (n,k,s)- perceptrons partition the input space V into s+1 regions with s parallel hyperplanes. We obtain results on the capacity of a single (n,k,s)-perceptron, respectively for V \subset Rn in general position and for V=K2. Finally, we describe a fast polynomial-time algorithm for counting the multilinear partitions of K2.
INDEX TERMS
Farey sequences, partition, separability, k-valued s- threshold perceptron, (k, k)-grid, minimal pair, multiple-valued logic, general position, complexity.
CITATION

I. Stojmenovic, A. Ngom and J. Zunic, "On the Number of Multilinear Partitions and the Computing Capacity of Multiple-Valued Multiple-Threshold Perceptrons.," Proceedings 1999 29th IEEE International Symposium on Multiple-Valued Logic (Cat. No.99CB36329)(ISMVL), Freiburg im Breisgau, Germany, 1999, pp. 208.
doi:10.1109/ISMVL.1999.779718
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