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- W2086920199 abstract "Abstract In this paper a new, very fast, simple and computationally effective algorithm to generate the minimal Reed-Muller Exclusive OR (ExOR) expansion with mixed polarity for any arbitrary, completely and incompletely specified switching function. The major consideration of this algorithm is to obtain a minimum number of product terms in the ExOR function. The algorithm is based on the use of Boolean matrix representation and an efficient technique called “minterm separation operation” developed by the author. The proposed algorithm consists of three procedures: (1) removing the variables on which a given switching function does not depend; (2) generating the positive polarity Reed-Muller expansion coefficients; and then (3) generating the final Reed-Muller ExOR expansion with mixed polarity in the canonical product form directly. A procedure for handling incompletely specified functions to deduce the suitable selection of “Don't care” terms is combined with Procedure 1 and/or Procedure 2. The proposed algorithm can deal with functions of large number of variables because there is no restriction from the algorithm on the number of variables within any given function. Based on the proposed approach, a fast and efficient computer program is developed. This computer program accepts an arbitrary switching function in terms of minterms and returns a mixed-polarity Reed-Muller expansion as an output in its canonical product form. The realization of the developed algorithm and the computer implementation was tested on many examples from the literature as well as on many arithmetic functions. On all examples the solutions were either the same or better than those generated by other methods." @default.
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- W2086920199 date "1993-05-01" @default.
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- W2086920199 title "Efficient and fast algorithm to generate minimal Reed-Muller Exclusive-OR expansions with mixed polarity for completely and incompletely specified functions and its computer implementation" @default.
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- W2086920199 doi "https://doi.org/10.1016/0045-7906(93)90002-9" @default.
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