New information on the effectiveness of different reed-muller algebras on the representation of quaternary functions

机译：有关不同里德穆勒代数对四元函数表示的有效性的新信息

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Efforts to get reliable data about the efficiency of a set of basis functions in representing a Reed-Muller canonical form with the minimum number of coefficients are frustrated by the long computation times necessary for calculation. Using an integrated suite of utility programs employing fast transforms, we provide statistics on the performance of six different algebras for two, three, four and five variables. Based on experimental results we suggest that the choice of basis functions has only a marginal effect for random samples from the entire function space. In addition we provide evidence which suggests that providing additional polarities has a more and more marginal effect upon efficiency.

机译：为了获得可靠的数据，这些数据对于以最小的系数表示Reed-Muller规范形式的一组基函数的效率是很困难的，这是因为计算所需的较长计算时间而感到沮丧。使用一套采用快速变换的实用程序的集成套件，我们为两个，三个，四个和五个变量提供了六个不同代数的性能统计信息。根据实验结果，我们建议选择基函数仅对整个函数空间中的随机样本具有边际效应。此外，我们提供的证据表明，提供更多的极性对效率有越来越大的边际影响。

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《Multiple-Valued Logic, 2003. Proceedings. 33rd International Symposium on》|2003年|p.33-39|共7页
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Adams K.J.; McGregor J.;
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中图分类无线电电子学、电信技术;
关键词
matrix algebra; transforms; multivalued logic; random functions; statistics; minimisation; Reed-Muller canonical form; utility programs; fast transforms; Reed-Muller algebras; quaternary functions;

机译：矩阵代数;变换;多值逻辑;随机函数;统计量;最小化; Reed-Muller规范形式;实用程序;快速变换; Reed-Muller代数;四元函数;

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2. Reed-Muller Representation of Symmetric Functions [J] . EKATERINA POGOSSOVA, KAREN EGIAZARIAN Journal of multiple-valued logic and soft computing . 2004,第1期

机译：对称函数的Reed-Muller表示
3. Computation of Reed-Muller expansions of incompletely specified Boolean functions from reduced representations [J] . Varma D., Trachtenberg E.A. IEE Proceedings. Part E . 1991,第2期

机译：从简化表示中计算不完全指定的布尔函数的Reed-Muller展开
4. New Information on the Effectiveness of Different Reed-Muller Algebras on the Representation of Quaternary Functions [C] . KJ. Adams, J. McGregor International Symposium on Multiple-Valued Logic . 2002

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5. Relationship of college students' visual preference to use of representations: Conceptual understanding of *functions in algebra. [D] . Herman, Marlena Faith. 2002

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7. Pseudo-trace functions for vertex operator algebras and Zhu's algebras (Research into Finite Groups and their Representations, Vertex Operator Algebras, and Combinatorics) [O] . 有家雄介 2012

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New information on the effectiveness of different reed-muller algebras on the representation of quaternary functions

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