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Algebraic and Combinatorial Methods for Reducing the Number of Variables of Partially Defined Discrete Functions

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Details

Original languageEnglish
Title of host publicationProceedings - 2017 IEEE 47th International Symposium on Multiple-Valued Logic, ISMVL 2017
PublisherIEEE
Pages167-172
Number of pages6
ISBN (Electronic)9781509054954
DOIs
Publication statusPublished - 30 Jun 2017
Publication typeA4 Article in a conference publication
EventIEEE INTERNATIONAL SYMPOSIUM ON MULTIPLE-VALUED LOGIC -
Duration: 1 Jan 1900 → …

Publication series

Name
ISSN (Electronic)2378-2226

Conference

ConferenceIEEE INTERNATIONAL SYMPOSIUM ON MULTIPLE-VALUED LOGIC
Period1/01/00 → …

Abstract

Applications of pattern recognition, design of faulttolerant systems and communications have key problems that arenaturally described by partially defined (incompletely defined)discrete functions. Such partially defined functions arising frompractical demands usually have a large number of variables andso their direct implementations require complex systems. Thusit is important to have at hand an efficient method to reducethe number of their variables. Here we review recent results tolinearly decompose a discrete function using a transform thatcan be efficiently implemented as a Galois field deconvolution. We also study the question: What are the general bounds for thedimension of the range space for an arbitrary linear transformto reduce a partially defined discrete function? We derive abound for the dimension of the range for arbitrary lineartransformation. We also estimate how good linear decompositioncan be obtained by the use of random transformations and showthat with a randomly generated transform we can reach theabove discussed bound.

ASJC Scopus subject areas

Keywords

  • index generation function, linear decomposition, partially defined function

Publication forum classification

Field of science, Statistics Finland