scholarly journals Reconstruction of Full Rank Algebraic Branching Programs

2019 ◽  
Vol 11 (1) ◽  
pp. 1-56
Author(s):  
Neeraj Kayal ◽  
Vineet Nair ◽  
Chandan Saha ◽  
Sébastien Tavenas
Keyword(s):  
Full Rank ◽  
Branching Programs ◽  
Algebraic Branching Programs

Average-case linear matrix factorization and reconstruction of low width algebraic branching programs

2019 ◽  
Vol 28 (4) ◽  
pp. 749-828 ◽  
Author(s):  
Neeraj Kayal ◽  
Vineet Nair ◽  
Chandan Saha
Keyword(s):  
Matrix Factorization ◽  
Linear Matrix ◽  
Branching Programs ◽  
Average Case ◽  
Algebraic Branching Programs

scholarly journals On Algebraic Branching Programs of Small Width

2018 ◽  
Vol 65 (5) ◽  
pp. 1-29 ◽  
Keyword(s):  
Branching Programs ◽  
Algebraic Branching Programs ◽  
Small Width

scholarly journals Separation Between Read-once Oblivious Algebraic Branching Programs (ROABPs) and Multilinear Depth-three Circuits

2020 ◽  
Vol 12 (1) ◽  
pp. 1-27
Author(s):  
Neeraj Kayal ◽  
Vineet Nair ◽  
Chandan Saha
Keyword(s):  
Branching Programs ◽  
Algebraic Branching Programs

scholarly journals A quadratic lower bound for homogeneous algebraic branching programs

2019 ◽  
Vol 28 (3) ◽  
pp. 409-435
Author(s):  
Mrinal Kumar
Keyword(s):  
Lower Bound ◽  
Branching Programs ◽  
Algebraic Branching Programs

On the power of algebraic branching programs of width two

2015 ◽  
Vol 25 (1) ◽  
pp. 217-253 ◽  
Author(s):  
Eric Allender ◽  
Fengming Wang
Keyword(s):  
Branching Programs ◽  
Algebraic Branching Programs

Variants of Homomorphism Polynomials Complete for Algebraic Complexity Classes

2021 ◽  
Vol 13 (4) ◽  
pp. 1-26
Author(s):  
Prasad Chaugule ◽  
Nutan Limaye ◽  
Aditya Varre
Keyword(s):  
Complexity Classes ◽  
Algebraic Complexity ◽  
Branching Programs ◽  
Algebraic Branching Programs ◽  
Graph Homomorphisms ◽  
Model Independent ◽  
Injective Homomorphisms

We present polynomial families complete for the well-studied algebraic complexity classes VF, VBP, VP, and VNP. The polynomial families are based on the homomorphism polynomials studied in the recent works of Durand et al. (2014) and Mahajan et al. (2018). We consider three different variants of graph homomorphisms, namely injective homomorphisms , directed homomorphisms , and injective directed homomorphisms , and obtain polynomial families complete for VF, VBP, VP, and VNP under each one of these. The polynomial families have the following properties: • The polynomial families complete for VF, VBP, and VP are model independent, i.e., they do not use a particular instance of a formula, algebraic branching programs, or circuit for characterising VF, VBP, or VP, respectively. • All the polynomial families are hard under p -projections.

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