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Abstract-We consider the problem of testing if a given function f:F2n → F2 is close to any degree d polynomial in n variables, also known as the Reed-Muller testing problem. Alon et al. [1] proposed and analyzed a natural 2d+1-query test for this problem. This test turned out to be intimately related to the Gowers norm. Alon et. al. showed that this test accepts every degree d polynomial with probability...
In this paper we give the first construction of a pseudorandom generator, with seed length O(log n), for CC0[p], the class of constant-depth circuits with unbounded fan-in MODp gates, for some prime p. More accurately, the seed length of our generator is O(log n) for any constant error ϵ > 0. In fact, we obtain our generator by fooling distributions generated by low degree polynomials, over Fp,...
We prove a quantitative version of the Gibbard-Satterthwaite theorem. We show that a uniformly chosen voter profile for a neutral social choice function f of q ≥ 4 alternatives and n voters will be manipulable with probability at least 10-4∈2n-3q-30, where e is the minimal statistical distance between / and the family of dictator functions. Our results extend those of, which were obtained for the...
Describing social positions and roles is an important topic within social network analysis. One approach is to compute a suitable equivalence relation on the nodes of the target network. One relation that is often used for this purpose is regular equivalence, or bisimulation, as it is known within the field of computer science. In this paper we consider a relation from computer science called simulation...
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