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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