Authors: Stanković, Radomir 
Moraga, Claudio
Astola, Jaakko
Title: Derivatives for multiple-valued functions induced by galois field and reed-muller-fourier expressions
Journal: Proceedings of The International Symposium on Multiple-Valued Logic
First page: 184
Last page: 189
Conference: 34th International Symposium on Multiple-Values Logic, ISMVL 2004; Toronto, Ont; Canada; 19 May 2004 through 22 May 2004
Issue Date: 26-Jul-2004
ISBN: 978-0-7695-2130-4
ISSN: 0195-623X
DOI: 10.1109/ISMVL.2004.1319939
Abstract: 
In classical mathematics, Newton-Leibniz differential operators determine coefficients in Taylor series. At the same time, there are relationships between Fourier coefficients of a (differentiable) function and its derivative. By the analogy, Boolean differential operators are viewed as coefficients of Taylor-Maclaurin series-like expressions for switching functions, usually dented as Reed-Muller expressions. Spectral interpretation of these expressions, permits to relate the Boolean difference to the coefficients in Fourier series-like expressions for switching functions. This paper considers these two possible ways of introduction of differential operators for multiple-valued (MV) functions. We defined the Logic derivatives and Gibbs derivatives for MV functions as coefficients in Taylor-Maclaurin series for MV functions and through relationships to Fourier series-like coefficients, respectively.
Publisher: IEEE

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