Strongly Exponential Separation between Monotone VP and Monotone VNP
نویسندگان
چکیده
منابع مشابه
The gap between monotone and non-monotone circuit complexity is exponential
The lower bound (b) has been improved to a properly exponential function (exp (cn~)) by N. Alon and R. Boppana [1]. It is a conceptual advantage of (a) that the problem considered there is polynomial time solvable and therefore can be computed by a polynomial size nonmonotone Boolean circuit, thus establishing a superpolynomial gap between the monotone and non-monotone circuit complexities of m...
متن کاملBoundaries of VP and VNP
One fundamental question in the context of the geometric complexity theory approach to the VP vs. VNP conjecture is whether VP = VP, where VP is the class of families of polynomials that can be computed by arithmetic circuits of polynomial degree and size, and VP is the class of families of polynomials that can be approximated infinitesimally closely by arithmetic circuits of polynomial degree ...
متن کاملStrongly Monotone Drawings of Planar Graphs
A straight-line drawing of a graph is a monotone drawing if for each pair of vertices there is a path which is monotonically increasing in some direction, and it is called a strongly monotone drawing if the direction of monotonicity is given by the direction of the line segment connecting the two vertices. We present algorithms to compute crossing-free strongly monotone drawings for some classe...
متن کاملStrongly Fejer Monotone Mappings Part I : Relaxations
We consider the general class of strongly Fejer monotone map-pings and some of their basic properties. These properties are useful for a convergence theory of corresponding iterative methods which are widely used to solve convex problems (see e.g. 3], 6], 7], 10]). In part I we study the relation between these mappings and their relaxations. 1 Strongly Fejer monotone mappings Let H be a (real) ...
متن کاملVNP=VP in the multilinear world
In this note, we show that over fields of any characteristic, exponential sums of Boolean instantiations of polynomials computed by multilinear circuits can be computed by multilinear circuits with polynomial blow-up in size. In particular, multilinear-VNP equals multilinear-VP. Our result showing closure under exponential sums also holds for other restricted multilinear classes – polynomials c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ACM Transactions on Computation Theory
سال: 2020
ISSN: 1942-3454,1942-3462
DOI: 10.1145/3417758