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A Karnaugh map (KM or K-map) is a diagram that can be used to simplify a Boolean algebra expression. Maurice Karnaugh introduced it in 1953 [ 1 ] [ 2 ] as a refinement of Edward W. Veitch 's 1952 Veitch chart , [ 3 ] [ 4 ] which itself was a rediscovery of Allan Marquand 's 1881 logical diagram [ 5 ] [ 6 ] (aka.
For a function of n variables the number of prime implicants can be as large as /, [25] e.g. for 32 variables there may be over 534 × 10 12 prime implicants. Functions with a large number of variables have to be minimized with potentially non-optimal heuristic methods, of which the Espresso heuristic logic minimizer was the de facto standard ...
A multilinear map of one variable is a linear map, and of two variables is a bilinear map. More generally, for any nonnegative integer , a multilinear map of k variables is called a k-linear map. If the codomain of a multilinear map is the field of scalars, it is called a multilinear form.
Because a + b + c = K for all substances being graphed, any one variable is not independent of the others, so only two variables must be known to find a sample's point on the graph: for instance, c must be equal to K − a − b. Because the three numerical values cannot vary independently—there are only two degrees of freedom—it is ...
For 3 variables, Brenner et al. applied multivariate mutual information to neural coding and called its negativity "synergy" [15] and Watkinson et al. applied it to genetic expression. [16] For arbitrary k variables, Tapia et al. applied multivariate mutual information to gene expression. [17] [14] It can be zero, positive, or negative. [13]
The current example illustrations of K maps on this page are atrociously har to read due to the coloration system used. Such simple examples are made so awfully difficult to make out. I propose replacing these with normal, standard K map illustrations that use colored outlines and no shading. 152.3.68.83 19:26, 5 March 2013 (UTC) Agreed.
Those 16 numbers correspond to the minterms of Image:K-map minterms.svg used in a 4-variable [[:en:Karnaugh map File usage No pages on the English Wikipedia use this file (pages on other projects are not listed).
Graphs of maps, especially those of one variable such as the logistic map, are key to understanding the behavior of the map. One of the uses of graphs is to illustrate fixed points, called points. Draw a line y = x (a 45° line) on the graph of the map. If there is a point where this 45° line intersects with the graph, that point is a fixed point.