Abstract
We study the complexity of realization of Boolean functions by circuits of functional gates over the infinite basis AC consisting of all antichain Boolean functions, i.e.,the functions taking the value 1 only at pairwise incomparable tuples. It is shown thatas n → ∞ the complexity of realization of a linear function of n arguments over thebasis AC grows at least as (n/ log n)1/2. It is established that the maximal complexity of realization of Boolean functions of n arguments over the basis AC grows at least as (n/log n)1/2 and at most as n.
This research was supported by the Russian Foundation for Basic Research (Grant 93-01-01527).
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References
O. M. Kasim-Zade (1994) On the complexity of circuits over an infinite basis (in Russian), Vestnik Moskov. Univ. Ser. I Mat. Mekh. No. 6, 40–44.
M. Aigner (1979) Combinatorial Theory, Springer-Verlag, Berlin etc.
G. P. Gavrilov and A. A. Sapozhenko (1977) Problem Book in Discrete Math ematics (in Russian), Nauka, Moscow.
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© 1997 Springer Science+Business Media Dordrecht
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Kasim-Zade, O.M. (1997). On the Complexity of Realization of Boolean Functions by Circuits Over an Infinite Basis. In: Operations Research and Discrete Analysis. Mathematics and Its Applications, vol 391. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5678-3_7
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DOI: https://doi.org/10.1007/978-94-011-5678-3_7
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