منابع مشابه
Testing Coverage Functions
A coverage function f over a ground set [m] is associated with a universe U of weighted elements and m sets A1, . . . , Am ⊆ U , and for any T ⊆ [m], f(T ) is defined as the total weight of the elements in the union ∪j∈TAj . Coverage functions are an important special case of submodular functions, and arise in many applications, for instance as a class of utility functions of agents in combinat...
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We study the problem of approximating and learning coverage functions. A function c : 2 → R is a coverage function, if there exists a universe U with non-negative weights w(u) for each u ∈ U and subsets A1, A2, . . . , An of U such that c(S) = ∑ u∈∪i∈SAi w(u). Alternatively, coverage functions can be described as non-negative linear combinations of monotone disjunctions. They are a natural subc...
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Let Fq be a finite field and f(x) ∈ Fq(x) be a rational function over Fq. The decision problem PermFunction consists of deciding whether f(x) induces a permutation on the elements of Fq. That is, we want to decide whether the corresponding map f : Fq 7→ Fq defined by a 7→ f(a) is a bijective mapping or not. This problem was known to be in ZPP but not known to be in P. We resolve the complexity ...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2015
ISSN: 0895-4801,1095-7146
DOI: 10.1137/140964072