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An algebraic approach to reducing the number of variables of incompletely defined discrete functions

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

Details

Original languageEnglish
Title of host publication2016 IEEE 46th International Symposium on Multiple-Valued Logic, ISMVL 2016
PublisherIEEE
Pages107-112
Number of pages6
ISBN (Electronic)9781467394888
DOIs
Publication statusPublished - 18 Jul 2016
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

In this paper, we consider incompletely defined discrete functions, i.e., Boolean and multiple-valued functions, f: S→ {0,1,,q - 1} where S ⊂ {0,1,,q - 1}n i.e., the function value is specified only on a certain subset S of the domain of the corresponding completely defined function. We assume the function to be sparse i.e. is 'small' relative to the cardinality of the domain. We show that by embedding the domain {0,1,,q - 1}n, where n is the number of variables and q is a prime power, in a suitable ring structure, the multiplicative structure of the ring can be used to construct a linear function {0,1,,q - 1}n → {0,1,,q - 1}m that is injective on S provided that m > 2logq|S|+logq(n - 1). In this way we find a linear transform that reduces the number of variables from n to m, and can be used e.g. in implementation of an incompletely defined discrete function by using linear decomposition.

ASJC Scopus subject areas

Keywords

  • index generation functions, multiple valued functions, reduction of variables

Publication forum classification

Field of science, Statistics Finland