TY - GEN
T1 - Improved composition theorems for functions and relations
AU - Koroth, Sajin
AU - Meir, Or
N1 - Publisher Copyright: © 2018 Aditya Bhaskara and Srivatsan Kumar.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - One of the central problems in complexity theory is to prove super-logarithmic depth bounds for circuits computing a problem in P, i.e., to prove that P is not contained in NC1. As an approach for this question, Karchmer, Raz and Wigderson [5] proposed a conjecture called the KRW conjecture, which if true, would imply that P is not cotained in NC1. Since proving this conjecture is currently considered an extremely difficult problem, previous works by Edmonds, Impagliazzo, Rudich and Sgall [1], Håstad and Wigderson [3] and Gavinsky, Meir, Weinstein and Wigderson [2] considered weaker variants of the conjecture. In this work we significantly improve the parameters in these variants, achieving almost tight lower bounds.
AB - One of the central problems in complexity theory is to prove super-logarithmic depth bounds for circuits computing a problem in P, i.e., to prove that P is not contained in NC1. As an approach for this question, Karchmer, Raz and Wigderson [5] proposed a conjecture called the KRW conjecture, which if true, would imply that P is not cotained in NC1. Since proving this conjecture is currently considered an extremely difficult problem, previous works by Edmonds, Impagliazzo, Rudich and Sgall [1], Håstad and Wigderson [3] and Gavinsky, Meir, Weinstein and Wigderson [2] considered weaker variants of the conjecture. In this work we significantly improve the parameters in these variants, achieving almost tight lower bounds.
KW - Circuit Complexity
KW - Communication Complexity
KW - Composition
KW - KRW Conjecture
UR - http://www.scopus.com/inward/record.url?scp=85052438983&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.APPROX-RANDOM.2018.48
DO - 10.4230/LIPIcs.APPROX-RANDOM.2018.48
M3 - Conference contribution
SN - 9783959770859
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018
A2 - Blais, Eric
A2 - Rolim, Jose D. P.
A2 - Steurer, David
A2 - Jansen, Klaus
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 21st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2018 and the 22nd International Workshop on Randomization and Computation, RANDOM 2018
Y2 - 20 August 2018 through 22 August 2018
ER -