Complexity theory column 88: Challenges in polynomial factorization1
MA Forbes, A Shpilka - ACM SIGACT News, 2015 - dl.acm.org
Algebraic complexity theory studies the complexity of computing (multivariate) polynomials
efficiently using algebraic circuits. This succinct representation leads to fundamental …
efficiently using algebraic circuits. This succinct representation leads to fundamental …
Proof complexity lower bounds from algebraic circuit complexity
MA Forbes, A Shpilka, I Tzameret… - arxiv preprint arxiv …, 2016 - arxiv.org
We give upper and lower bounds on the power of subsystems of the Ideal Proof System
(IPS), the algebraic proof system recently proposed by Grochow and Pitassi, where the …
(IPS), the algebraic proof system recently proposed by Grochow and Pitassi, where the …
Towards identity testing for sums of products of read-once and multilinear bounded-read formulae
An arithmetic formula is an arithmetic circuit where each gate has fan-out one. An arithmetic
read-once formula (ROF in short) is an arithmetic formula where each input variable labels …
read-once formula (ROF in short) is an arithmetic formula where each input variable labels …
Proof complexity lower bounds from algebraic circuit complexity
MA Forbes, A Shpilka, I Tzameret… - Theory of …, 2021 - theoryofcomputing.org
We give upper and lower bounds on the power of subsystems of the Ideal Proof System
(IPS), the algebraic proof system recently proposed by Grochow and Pitassi (J. ACM, 2018) …
(IPS), the algebraic proof system recently proposed by Grochow and Pitassi (J. ACM, 2018) …
Limitations of sum of products of read-once polynomials
We study limitations of polynomials computed by depth two circuits built over read-once
polynomials (ROPs) and depth three syntactically multi-linear formulas. We prove an …
polynomials (ROPs) and depth three syntactically multi-linear formulas. We prove an …
On verifying proofs in constant depth, and polynomial identity testing [HBNI Th76]
K Sreenivasaiah - 2015 - imsc.res.in
This thesis is divided into two main parts. The first part deals with proof systems computable
by Boolean circuit families that characterize the complexity class NC0 (bounded fanin …
by Boolean circuit families that characterize the complexity class NC0 (bounded fanin …
[PDF][PDF] On verifying proofs in constant depth, and polynomial identity testing
K Sreenivasaiah - 2014 - hbni.ac.in
The thesis is divided into two main parts. The first part deals with proof systems computable
by Boolean circuit families that characterize the complexity class NC0 (bounded fanin …
by Boolean circuit families that characterize the complexity class NC0 (bounded fanin …