منابع مشابه
A Lower Bound for Primality
Recent work by Bernasconi, Damm and Shparlinski showed that the set of square-free numbers is not in AC, and raised as an open question if similar (or stronger) lower bounds could be proved for the set of prime numbers. In this note, we show that the Boolean majority function is AC-Turing reducible to the set of prime numbers (represented in binary). From known lower bounds on Maj (due to Razbo...
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Our most recent computations tell us that any counterexample to Giuga’s 1950 primality conjecture must have at least 19,908 decimal digits. Equivalently, any number which is both a Giuga and a Carmichael number must have at least 19,908 decimal digits. This bound has not been achieved through exhaustive testing of all numbers with up to 19,908 decimal digits, but rather through exploitation of ...
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In this paper, a new method for developing a lower bound on exact completion time distribution function of stochastic PERT networks is provided that is based on simplifying the structure of this type of network. The designed mechanism simplifies network structure by arc duplication so that network distribution function can be calculated only with convolution and multiplication. The selection of...
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Let A and B be two finite subsets of a field F. In this paper we provide a nontrivial lower bound for |{a + b: a ∈ A, b ∈ B, and P (a, b) 6= 0}| where P (x, y) ∈ F[x, y].
متن کاملA Lower Bound for
It is proved that there is a monotone function in AC(0) 4 which requires exponential size monotone perceptrons of depth 3. This solves the monotone version of a problem which, in the general case, would imply an oracle separation of PPPH.
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 2001
ISSN: 0022-0000
DOI: 10.1006/jcss.2000.1725