On the complexity of bounded-depth circuits and formulas over the basis of fan-in gates
2019 ◽
Vol 29
(4)
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pp. 241-254
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Abstract We obtain estimates for the complexity of the implementation of n-place Boolean functions by circuits and formulas built of unbounded fan-in conjunction and disjunction gates and either negation gates or negations of variables as inputs. Restrictions on the depth of circuits and formulas are imposed. In a number of cases, the estimates obtained in the paper are shown to be asymptotically sharp. In particular, for the complexity of circuits with variables and their negations on inputs, the Shannon function is asymptotically estimated as $2\cdot {{2}^{n/2}};$this estimate is attained on depth-3 circuits.
2018 ◽
Vol 28
(5)
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pp. 309-318
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1991 ◽
Vol 138
(1)
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pp. 48
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2018 ◽
Vol 26
(3)
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pp. 115-140
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2020 ◽
Vol E103.A
(12)
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pp. 1659-1665
2011 ◽
Vol E94-A
(6)
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pp. 1434-1440
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Vol E96.A
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pp. 1653-1656
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Vol E95.A
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pp. 1056-1064
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