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单词 Boolean Function
释义

Boolean Function

A Boolean function in variables is a function


where each can be 0 or 1 and is 0 or 1. Determining the number of monotone Boolean functions of variablesis known as Dedekind's Problem. The number of monotonic increasing Boolean functions of variables is given by2, 3, 6, 20, 168, 7581, 7828354, ... (Sloane's A000372, Beeler et al. 1972, Item 17). The number of inequivalent monotoneBoolean functions of variables is given by 2, 3, 5, 10, 30, ...(Sloane's A003182).


Let denote the number of distinct monotone Boolean functions of variables with mincuts. Then

 
 
 
 


References

Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972.

Sloane, N. J. A. SequencesA003182/M0729and A000372/M0817in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.


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