Authors: Astola, Jaakko
Astola, Pekka
Stanković, Radomir 
Tabus, Ioan
Title: An algebraic approach to reducing the number of variables of incompletely defined discrete functions
Journal: Proceedings of The International Symposium on Multiple-Valued Logic
Volume: 2016-July
First page: 107
Last page: 112
Conference: 46th IEEE International Symposium on Multiple-Valued Logic, ISMVL 2016; Sapporo, Hokkaido; Japan; 18 May 2016 through 20 May 2016
Issue Date: 18-Jul-2016
ISBN: 978-1-467-39488-8
ISSN: 0195-623X
DOI: 10.1109/ISMVL.2016.18
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.
Keywords: index generation functions | multiple valued functions | reduction of variables
Publisher: IEEE

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