On Algebraic Branching Programs of Small Width

doi:10.1145/3209663

Testing Membership in Languages that Have Small Width Branching Programs

SIAM Journal on Computing ◽

10.1137/s009753970038211x ◽

2002 ◽

Vol 31 (5) ◽

pp. 1557-1570 ◽

Cited By ~ 31

Author(s):

Ilan Newman

Keyword(s):

Branching Programs ◽

Small Width

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

Computational Complexity ◽

10.1007/s00037-019-00189-0 ◽

2019 ◽

Vol 28 (4) ◽

pp. 749-828 ◽

Cited By ~ 1

Author(s):

Neeraj Kayal ◽

Vineet Nair ◽

Chandan Saha

Keyword(s):

Matrix Factorization ◽

Linear Matrix ◽

Branching Programs ◽

Average Case ◽

Algebraic Branching Programs

Lower Bounds for Syntactically Multilinear Algebraic Branching Programs

Lecture Notes in Computer Science - Mathematical Foundations of Computer Science 2008 ◽

10.1007/978-3-540-85238-4_33 ◽

2008 ◽

pp. 407-418 ◽

Cited By ~ 8

Author(s):

Maurice J. Jansen

Keyword(s):

Lower Bounds ◽

Branching Programs ◽

Algebraic Branching Programs

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

ACM Transactions on Computation Theory ◽

10.1145/3369928 ◽

2020 ◽

Vol 12 (1) ◽

pp. 1-27

Author(s):

Neeraj Kayal ◽

Vineet Nair ◽

Chandan Saha

Keyword(s):

Branching Programs ◽

Algebraic Branching Programs

On the Power of Algebraic Branching Programs of Width Two

Automata, Languages and Programming - Lecture Notes in Computer Science ◽

10.1007/978-3-642-22006-7_62 ◽

2011 ◽

pp. 736-747 ◽

Cited By ~ 1

Author(s):

Eric Allender ◽

Fengming Wang

Keyword(s):

Branching Programs ◽

Algebraic Branching Programs

Reconstruction of Full Rank Algebraic Branching Programs

ACM Transactions on Computation Theory ◽

10.1145/3282427 ◽

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

A quadratic lower bound for homogeneous algebraic branching programs

Computational Complexity ◽

10.1007/s00037-019-00186-3 ◽

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

Computational Complexity ◽

10.1007/s00037-015-0114-7 ◽

2015 ◽

Vol 25 (1) ◽

pp. 217-253 ◽

Cited By ~ 2

Author(s):

Eric Allender ◽

Fengming Wang

Keyword(s):

Branching Programs ◽

Algebraic Branching Programs

Hitting sets for multilinear read-once algebraic branching programs, in any order

Proceedings of the 46th Annual ACM Symposium on Theory of Computing - STOC '14 ◽

10.1145/2591796.2591816 ◽

2014 ◽

Cited By ~ 15

Author(s):

Michael A. Forbes ◽

Ramprasad Saptharishi ◽

Amir Shpilka

Keyword(s):

Branching Programs ◽

Hitting Sets ◽

Algebraic Branching Programs

Variants of Homomorphism Polynomials Complete for Algebraic Complexity Classes

ACM Transactions on Computation Theory ◽

10.1145/3470858 ◽

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.