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A064436
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Number of switching functions of n or fewer variables which cannot be realized as threshold gates.
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5
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0, 0, 2, 152, 63654, 4294872724, 18446744073694523482, 340282366920938463463374607423390140592, 115792089237316195423570985008687907853269984665640564039457583990351590086990
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The corresponding systems of linear inequalities are not solvable: linearly non-separable truth or switching functions. Truth functions which ar "non-neurons" and are realizable only as two levels threshold gate networks.
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LINKS
| Wang Lan, Table of n, a(n) for n = 0...9
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FORMULA
| a(n)=2^(2^n)-A000609(n)
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EXAMPLE
| n=2: out of the 16 B^2 -> B^1 truth functions, 14 are linearly separable; the 2 exceptions are XOR and its negation: f[x,y]=!xz+x!y and !f[x,y]=xy+!x!y. So a(2)=2. With increasing n, the chance that a switching function belongs to this sequence tends to 1.
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CROSSREFS
| A000609.
Sequence in context: A113576 A102458 A206309 * A012605 A012602 A157087
Adjacent sequences: A064433 A064434 A064435 * A064437 A064438 A064439
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Oct 01 2001
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