Lower bound for monotone Boolean convolution
نویسنده
چکیده
Any monotone Boolean circuit computing the n-dimensional Boolean convolution requires at least n2 and-gates. This matches the obvious upper bound. The previous best bound for this problem was Ω(n4/3), obtained by Norbert Blum in 1981. More generally, exact bounds are given for all semi-disjoint bilinear forms.
منابع مشابه
Thin circulant matrices and lower bounds on the complexity of some Boolean operators
We prove a lower bound Ω ( k+l k2l2 N k+l+2 kl ) on the maximal possible weight of a (k, l)-free (that is, free of all-ones k × l submatrices) Boolean circulant N × N matrix. The bound is close to the known bound for the class of all (k, l)-free matrices. As a consequence, we obtain new bounds for several complexity measures of Boolean sums’ systems and a lower bound Ω(N2 log N) on the monotone...
متن کاملContinuous dependence on coefficients for stochastic evolution equations with multiplicative Levy Noise and monotone nonlinearity
Semilinear stochastic evolution equations with multiplicative L'evy noise are considered. The drift term is assumed to be monotone nonlinear and with linear growth. Unlike other similar works, we do not impose coercivity conditions on coefficients. We establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. As corollaries of ...
متن کاملMonotone and Boolean Convolutions for Non-compactly Supported Probability Measures
Abstract. The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the multiplicative boolean convolution of probability measures on the positive half-line is proposed. Unlike Bercovici’s multiplicative boolean convolution it ...
متن کاملSeparation of the Monotone NC Hierarchy
We prove tight lower bounds, of up to n , for the monotone depth of functions in monotone-P. As a result we achieve the separation of the following classes. 1. monotone-NC 6 = monotone-P. 2. For every i 1, monotone-NC i 6 = monotone-NC i+1. 3. More generally: For any integer function D(n), up to n (for some > 0), we give an explicit example of a monotone Boolean function, that can be computed b...
متن کاملA Lower Bound for Boolean Permanent in Bijective Boolean Circuits and its Consequences
We identify a new restriction on Boolean circuits called bijectivity and prove that bijective Boolean circuits require exponential size to compute the Boolean permanent function. As consequences of this lower bound, we show exponential size lower bounds for: (a) computing the Boolean permanent using monotone multilinear circuits ; (b) computing the 0-1 permanent function using monotone arithmet...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1708.03523 شماره
صفحات -
تاریخ انتشار 2017