Lower bounds for monotone counting circuits
نویسندگان
چکیده
منابع مشابه
Lower Bounds for Monotone Counting Circuits
A {+,×}-circuit counts a given multivariate polynomial f , if its values on 0-1 inputs are the same as those of f ; on other inputs the circuit may output arbitrary values. Such a circuit counts the number of monomials of f evaluated to 1 by a given 0-1 input vector (with multiplicities given by their coefficients). A circuit decides f if it has the same 0-1 roots as f . We first show that some...
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where ce ∈ N = {0, 1, 2, . . .}, and xi = 1. Produ ts ∏n i=1 x ei i are monomials of f ; we will often omit monomials whose oe ients ce are zero. The polynomial is multilinear, if ce = 0 for all e 6∈ {0, 1}n, and is homogeneous of degree d, if e1 + · · ·+ en = d for all e with ce 6= 0. A standard model of ompa t representation of su h polynomials (with nonnegative oe ients) is that of monotone ...
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We investigate monotone circuits with local oracles [Krajíček, 2016], i.e., circuits containing additional inputs yi = yi(~x) that can perform unstructured computations on the input string ~x. Let μ ∈ [0,1] be the locality of the circuit, a parameter that bounds the combined strength of the oracle functions yi(~x), and Un,k,Vn,k ⊆ {0,1}m be the set of k-cliques and the set of complete (k−1)-par...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2016
ISSN: 0166-218X
DOI: 10.1016/j.dam.2016.04.024