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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