Sensitivity, block sensitivity, and ℓ-block sensitivity of boolean functions
نویسندگان
چکیده
منابع مشابه
Sensitivity, block sensitivity, and l-block sensitivity of boolean functions
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...
متن کاملSensitivity block sensitivity and block sensitivity of boolean functions
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...
متن کاملSensitivity versus block sensitivity of Boolean functions
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.
متن کاملBlock Sensitivity of Weakly Symmetric Functions
Block sensitivity, which was introduced by Nisan [5], is one of the most useful measures of boolean functions. In this paper we investigate the block sensitivity of weakly symmetric functions (functions invariant under some transitive group action). We prove a Ω(N) lower bound for the block sensitivity of weakly symmetric functions. We also construct a weakly symmetric function which has block ...
متن کاملBlock sensitivity of minterm-transitive functions
Boolean functions with symmetry properties are interesting from a complexity theory perspective; extensive research has shown that these functions, if nonconstant, must have high ‘complexity’ according to various measures. In recent work of this type, Sun gave bounds on the block sensitivity of nonconstant Boolean functions invariant under a transitive permutation group. Sun showed that all suc...
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ژورنال
عنوان ژورنال: Information and Computation
سال: 2004
ISSN: 0890-5401
DOI: 10.1016/j.ic.2002.12.001