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For a Boolean function
given by a Boolean formula (or a binary circuit) S we discuss the problem of building a Boolean formula (binary circuit) of minimal size, which computes the function g equivalent to
, or -equivalent to
, i.e.,
. In this paper we prove that if P NP then this problem can not be approximated with a good approximation ratio by a polynomial time algorithm. 相似文献
2.
Binwu?Zhang Jianzhong?ZhangEmail author Yong?He 《Journal of Combinatorial Optimization》2005,9(2):187-198
In this paper, we consider the center location improvement problems under the sum-type and bottleneck-type Hamming distance. For the sum-type problem, we show that achieving an algorithm with a worst-case ratio of O(log |V|) is NP-hard, and for the bottleneck-type problem, we present a strongly polynomial algorithm. 相似文献
3.
Oleg A.?ProkopyevEmail author Panos M.?PardalosEmail author 《Journal of Combinatorial Optimization》2004,8(4):495-502
For a Boolean function f given by its truth table (of length
) and a parameter s the problem considered is whether there is a Boolean function g
-equivalent to f, i.e.,
, and computed by a circuit of size at most s. In this paper we investigate the complexity of this problem and show that for specific values of
it is unlikely to be in P/poly. Under the same assumptions we also consider the optimization variant of the problem and prove its inapproximability. 相似文献
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