Add to ORKGWe show that the two main reduction notions in arithmetic circuit complexity, p-projections and c-reductions, differ in power. We do so by showing unconditionally that there are polynomials that are VNP-complete under c-reductions but not under p-projections. We also show that the question of which polynomials are VNP-complete under which type of reductions depends on the underlying field
The Minimum Circuit Size Problem (MCSP) is: given the truth table of a Boolean function f and a size...
AbstractBy using arithmetic circuits, encoding multivariate polynomials may be drastically more effi...
This paper presents the following results on sets that are complete for $NP$. begin{enumerate} item...
We show that the two main reduction notions in arithmetic circuit complexity, p-projections and c-re...
In 1979 Valiant introduced the complexity class VNP of p-definable families of polynomials, he defin...
Arithmetic complexity is the study of the required ressources for computing poynomials using only ar...
16 pagesBy using arithmetic circuits, encoding multivariate polynomials may be drastically more effi...
We say that a circuit C over a field F {functionally} computes a polynomial P in F[x_1, x_2, ..., x_...
AbstractUnder the assumption that NP does not have p-measure 0, we investigate reductions to NP-comp...
We study the Minimum Circuit Size Problem (MCSP): given the truth-table of a Boolean function f and ...
Assuming that the Permanent polynomial requires algebraic circuits of exponential size, we show that...
One fundamental question in the context of the geometric complexity theory approach to the VP vs. VN...
An account of Valiant's theory of p-computable versus p-definable polynomials, an arithmetic analogu...
In Valiant developed an algebraic analogue of the theory of NP-completeness for computations of po...
Arithmetic Circuits compute polynomial functions over their inputs via a sequence of arithmetic oper...
The Minimum Circuit Size Problem (MCSP) is: given the truth table of a Boolean function f and a size...
AbstractBy using arithmetic circuits, encoding multivariate polynomials may be drastically more effi...
This paper presents the following results on sets that are complete for $NP$. begin{enumerate} item...
We show that the two main reduction notions in arithmetic circuit complexity, p-projections and c-re...
In 1979 Valiant introduced the complexity class VNP of p-definable families of polynomials, he defin...
Arithmetic complexity is the study of the required ressources for computing poynomials using only ar...
16 pagesBy using arithmetic circuits, encoding multivariate polynomials may be drastically more effi...
We say that a circuit C over a field F {functionally} computes a polynomial P in F[x_1, x_2, ..., x_...
AbstractUnder the assumption that NP does not have p-measure 0, we investigate reductions to NP-comp...
We study the Minimum Circuit Size Problem (MCSP): given the truth-table of a Boolean function f and ...
Assuming that the Permanent polynomial requires algebraic circuits of exponential size, we show that...
One fundamental question in the context of the geometric complexity theory approach to the VP vs. VN...
An account of Valiant's theory of p-computable versus p-definable polynomials, an arithmetic analogu...
In Valiant developed an algebraic analogue of the theory of NP-completeness for computations of po...
Arithmetic Circuits compute polynomial functions over their inputs via a sequence of arithmetic oper...
The Minimum Circuit Size Problem (MCSP) is: given the truth table of a Boolean function f and a size...
AbstractBy using arithmetic circuits, encoding multivariate polynomials may be drastically more effi...
This paper presents the following results on sets that are complete for $NP$. begin{enumerate} item...