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Demystifying the border of depth-3 algebraic circuits
Border complexity of polynomials plays an integral role in GCT (Geometric Complexity
Theory) approach to P versus NP. It tries to formalize the notion of 'approximating a …
Theory) approach to P versus NP. It tries to formalize the notion of 'approximating a …
Hitting sets and reconstruction for dense orbits in vp_ {e} and ΣΠΣ circuits
In this paper we study polynomials in VP_ {e}(polynomial-sized formulas) and in ΣΠΣ
(polynomial-size depth-3 circuits) whose orbits, under the action of the affine group GL^{aff} …
(polynomial-size depth-3 circuits) whose orbits, under the action of the affine group GL^{aff} …
[PDF][PDF] Completeness classes in algebraic complexity theory
arxiv:2406.06217v1 [cs.CC] 10 Jun 2024 Page 1 COMPLETENESS CLASSES IN
ALGEBRAIC COMPLEXITY THEORY PETER BÜRGISSER Abstract. The purpose of this …
ALGEBRAIC COMPLEXITY THEORY PETER BÜRGISSER Abstract. The purpose of this …
Hitting sets for orbits of circuit classes and polynomial families
The orbit of an n-variate polynomial over a field is the set. The orbit of a polynomial f is a
geometrically interesting subset of the set of affine projections of f. Affine projections of …
geometrically interesting subset of the set of affine projections of f. Affine projections of …
Fixed-parameter debordering of Waring rank
Border complexity measures are defined via limits (or topological closures), so that any
function which can approximated arbitrarily closely by low complexity functions itself has low …
function which can approximated arbitrarily closely by low complexity functions itself has low …
[كتاب][B] Algebraic complexity, asymptotic spectra and entanglement polytopes
J Zuiddam - 2018 - eprints.illc.uva.nl
Matrix rank is well-known to be multiplicative under the Kronecker product, additive under
the direct sum, normalised on identity matrices and non-increasing under multiplying from …
the direct sum, normalised on identity matrices and non-increasing under multiplying from …
Succinct hitting sets and barriers to proving lower bounds for algebraic circuits
We formalize a framework of algebraically natural lower bounds for algebraic circuits. Just
as with the natural proofs notion of Razborov and Rudich (1997) for Boolean circuit lower …
as with the natural proofs notion of Razborov and Rudich (1997) for Boolean circuit lower …
Discovering the roots: Uniform closure results for algebraic classes under factoring
Newton iteration (NI) is an almost 350 years old recursive formula that approximates a
simple root of a polynomial quite rapidly. We generalize it to a matrix recurrence (allRootsNI) …
simple root of a polynomial quite rapidly. We generalize it to a matrix recurrence (allRootsNI) …
On the power of border of depth-3 arithmetic circuits
We show that over the field of complex numbers, every homogeneous polynomial of degree
d can be approximated (in the border complexity sense) by a depth-3 arithmetic circuit of top …
d can be approximated (in the border complexity sense) by a depth-3 arithmetic circuit of top …
Implementing geometric complexity theory: On the separation of orbit closures via symmetries
C Ikenmeyer, U Kandasamy - Proceedings of the 52nd Annual ACM …, 2020 - dl.acm.org
Understanding the difference between group orbits and their closures is a key difficulty in
geometric complexity theory (GCT): While the GCT program is set up to separate certain …
geometric complexity theory (GCT): While the GCT program is set up to separate certain …