Polynomial Threshold Functions, $AC^0 $ Functions, and Spectral Norms
نویسندگان
چکیده
منابع مشابه
Polynomial Threshold Functions, AC^0 Functions, and Spectral Norms
We study the class of polynomial threshold functions using harmonic analysis and apply the results to derive lower bounds related to ACo functions. A Boolean function is polynomial threshold if it can be represented as a sign function of a sparse polynomial (one that consists of a polynomial number of terms). Our main result is that the class of polynomial threshold functions can be characteriz...
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We study the complexity of computing Boolean functions on general Boolean domains by polynomial threshold functions (PTFs). A typical example of a general Boolean domain is {1, 2}. We are mainly interested in the length (the number of monomials) of PTFs, with their degree and weight being of secondary interest. We show that PTFs on general Boolean domains are tightly connected to depth two thre...
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We examine the spectra of boolean functions obtained as the sign of a real polynomial of degree d. A tight lower bound on various norms of the lower d levels of the function's Fourier transform is established. The result is applied to derive best possible lower bounds on the influences of variables on linear threshold functions. Some conjectures are posed concerning upper and lower bounds on in...
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We present a number of papers on topics in mathematics and theoretical computer science. Topics include: a problem relating to the ABC Conjecture, the ranks of 2-Selmer groups of twists of an elliptic curve, the Goldbach problem for primes in specified Chebotarev classes, explicit models for Deligne-Lusztig curves, constructions for small designs, noise sensitivity bounds for polynomials thresh...
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We study the computational power of polynomial threshold functions, that is, threshold functions of real polynomials over the boolean cube. We provide two new results bounding the computational power of this model. Our first result shows that low-degree polynomial threshold functions cannot approximate any function with many influential variables. We provide a couple of examples where this tech...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 1992
ISSN: 0097-5397,1095-7111
DOI: 10.1137/0221003