Almost k-wise independence and hard Boolean functions
نویسندگان
چکیده
منابع مشابه
Almost k-Wise Independence and Hard Boolean Functions
Andreev et al gave constructions of Boolean functions computable by polynomial size circuits with large lower bounds for read once branching program b p s a function in P with the lower bound n polylog n a function in quasipolynomial time with the lower bound n O log n and a function in LINSPACE with the lower bound n log n O We point out alternative much simpler constructions of such Boolean f...
متن کاملAlmost k-wise independence versus k-wise independence
We say that a distribution over {0, 1} is ( , k)-wise independent if its restriction to every k coordinates results in a distribution that is -close to the uniform distribution. A natural question regarding ( , k)-wise independent distributions is how close they are to some k-wise independent distribution. We show that there exists ( , k)-wise independent distribution whose statistical distance...
متن کاملK-wise Independence and -biased K-wise Indepedence
1 Deenitions Consider a distribution D on n bits x = x 1 x n. D is k-wise independent ii for all sets of k indices S = fi 1 x ik = a 1 a k ] = 1 2 k : The idea is that if we restrict our attention to any k positions in x, no matter how many times we sample from D, we cannot distinguish D from the uniform distribution over n bits. We can get a Fourier interpretation of k-wise independence by vie...
متن کاملOn K-wise Independent Distributions and Boolean Functions
We pursue a systematic study of the following problem. Let f : {0, 1} → {0, 1} be a (usually monotone) boolean function whose behaviour is well understood when the input bits are identically independently distributed. What can be said about the behaviour of the function when the input bits are not completely independent, but only k-wise independent, i.e. every subset of k bits is independent? m...
متن کاملAlmost k-wise Independent Variables
We will now consider the problem of creating a set of bitstrings such that the bits are almost k-wise independent. Our method consists of two steps. In the first step we create a set of bitstrings such that parity on every fixed index set is almost even. In the second step we present a method to convert such a set into a set where the bits are almost k-wise independent. For presentational reaso...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2003
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(02)00643-6