On Block Sensitivity and Fractional Block Sensitivity
نویسندگان
چکیده
منابع مشابه
On Fractional Block Sensitivity
In this paper we study the fractional block sensitivity of Boolean functions. Recently, Tal [Tal13] and Gilmer, Saks, and Srinivasan [GSS13] independently introduced this complexity measure, denoted by fbs(f), and showed that it is equal (up to a constant factor) to the randomized certificate complexity, denoted by RC(f), which was introduced by Aaronson [Aar03]. In this paper, we relate the fr...
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Sensitivity is one of the simplest and block sensitivity one of the most useful invariants of a boolean function Nisan and Nisan and Szegedy have shown that block sensitivity is polynomially related to a number of measures of boolean function complexity The main open question is whether or not a polynomial relationship exists between sensitivity and block sensitivity We de ne the intermediate n...
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Sensitivity is one of the simplest, and block sensitivity one of the most useful, invariants of a boolean function. Nisan [SIAM J. Comput. 20 (6) (1991) 999] and Nisan and Szegedy [Comput. Complexity 4 (4) (1994) 301] have shown that block sensitivity is polynomially related to a number of measures of boolean function complexity. Themain open question is whether or not a polynomial relationship...
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Determining the maximal separation between sensitivity and block sensitivity of Boolean functions is of interest for computational complexity theory. We construct a sequence of Boolean functions with bs(f) = 1 2 s(f) 2 + 1 2 s(f). The best known separation previously was bs(f) = 1 2 s(f) 2 due to Rubinstein. We also report results of computer search for functions with at most 12 variables.
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Based on a recent characterization of nested canalyzing function (NCF), we obtain the formula of the sensitivity of any NCF. Hence we find that any sensitivity of NCF is between n+1 2 and n. Both lower and upper bounds are tight. We prove that the block sensitivity, hence the l-block sensitivity, is same to the sensitivity. It is well known that monotone function also has this property. We even...
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ژورنال
عنوان ژورنال: Lobachevskii Journal of Mathematics
سال: 2018
ISSN: 1995-0802,1818-9962
DOI: 10.1134/s1995080218070041