Koiran's real τ ‐conjecture claims that the number of real zeros of a structured polynomial given as a sum of m products of k real sparse polynomials, each with at most t monomials, is bounded by a polynomial in mkt . This conjecture has a major consequence in complexity theory since it would lead to superpolynomial lower bounds for the arithmetic circuit size of the permanent. We confirm the conjecture in a probabilistic sense by proving that if the coefficients involved in the description of f are independent standard Gaussian random variables, then the expected number of real zeros of f is .

中文翻译：

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真正的tau-conjecture平均而言是正确的

Koiran真实τ -conjecture声称给出的和的结构多项式的实数零点的数目米产品ķ实稀疏的多项式，每个具有至多吨单项式，由多项式中界定MKT。该猜想在复杂性理论中具有重要意义，因为它将导致永久物的算术电路尺寸的超多项式下界。我们通过证明，如果参与的描述系数确定在概率意义上的猜想˚F是独立的标准高斯随机变量，那么真正的零的预期数量˚F是。