Monotone separations for constant degree
نویسندگان
چکیده
We prove a separation between monotone and general arithmetic formulas for polynomials of constant degree. We give an example of a polynomial C in n variables and degree k which is computable by an arithmetic formula of size O(k2n2), but every monotone formula computing C requires size (n/kc)Ω(log k), with c ∈ (0, 1). This also gives a separation between monotone and homogeneous formulas, for polynomials of constant degree.
منابع مشابه
Monotone separations for constant degree polynomials
We prove a separation between monotone and general arithmetic formulas for polynomials of constant degree. We give an example of a polynomial C in n variables and degree k which is computable by a homogeneous arithmetic formula of size O(k2n2), but every monotone formula computing C requires size (n/kc)Ω(log k), with c ∈ (0, 1). Since the upper bound is achieved by a homogeneous arithmetic form...
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تاریخ انتشار 2009