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Quine–McCluskey algorithm
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Quine–McCluskey algorithm : ウィキペディア英語版
Quine–McCluskey algorithm
The Quine–McCluskey algorithm (or the method of prime implicants) is a method used for minimization of boolean functions that was developed by W.V. Quine and extended by Edward J. McCluskey. It is functionally identical to Karnaugh mapping, but the tabular form makes it more efficient for use in computer algorithms, and it also gives a deterministic way to check that the minimal form of a Boolean function has been reached. It is sometimes referred to as the tabulation method.
The method involves two steps:
# Finding all prime implicants of the function.
# Use those prime implicants in a ''prime implicant chart'' to find the essential prime implicants of the function, as well as other prime implicants that are necessary to cover the function.
==Complexity==
Although more practical than Karnaugh mapping when dealing with more than four variables, the Quine–McCluskey algorithm also has a limited range of use since the problem it solves is NP-hard: the runtime of the Quine–McCluskey algorithm grows exponentially with the number of variables. It can be shown that for a function of ''n'' variables the upper bound on the number of prime implicants is 3''n''/''n''. If ''n'' = 32 there may be over 6.5
* 1015 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 is the de facto standard.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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