Improved composition theorems for functions and relations

Sajin Koroth; Or Meir

doi:10.4230/LIPIcs.APPROX-RANDOM.2018.48

Improved composition theorems for functions and relations

Sajin Koroth, Or Meir

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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.

Original language	English
Title of host publication	Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018
Editors	Eric Blais, Jose D. P. Rolim, David Steurer, Klaus Jansen
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Print)	9783959770859
DOIs	https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2018.48
State	Published - 1 Aug 2018
Event	21st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2018 and the 22nd International Workshop on Randomization and Computation, RANDOM 2018 - Princeton, United States Duration: 20 Aug 2018 → 22 Aug 2018

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	116
ISSN (Print)	1868-8969

Conference

Conference	21st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2018 and the 22nd International Workshop on Randomization and Computation, RANDOM 2018
Country/Territory	United States
City	Princeton
Period	20/08/18 → 22/08/18

Bibliographical note

Publisher Copyright:
© 2018 Aditya Bhaskara and Srivatsan Kumar.

Keywords

Circuit Complexity
Communication Complexity
Composition
KRW Conjecture

ASJC Scopus subject areas

Software

Access to Document

10.4230/LIPIcs.APPROX-RANDOM.2018.48

Cite this

Koroth, S., & Meir, O. (2018). Improved composition theorems for functions and relations. In E. Blais, J. D. P. Rolim, D. Steurer, & K. Jansen (Eds.), Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018 Article 48 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 116). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2018.48

Koroth, Sajin ; Meir, Or. / Improved composition theorems for functions and relations. Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018. editor / Eric Blais ; Jose D. P. Rolim ; David Steurer ; Klaus Jansen. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. (Leibniz International Proceedings in Informatics, LIPIcs).

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abstract = "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], H{\aa}stad 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.",

keywords = "Circuit Complexity, Communication Complexity, Composition, KRW Conjecture",

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note = "Publisher Copyright: {\textcopyright} 2018 Aditya Bhaskara and Srivatsan Kumar.; 21st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2018 and the 22nd International Workshop on Randomization and Computation, RANDOM 2018 ; Conference date: 20-08-2018 Through 22-08-2018",

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Koroth, S & Meir, O 2018, Improved composition theorems for functions and relations. in E Blais, JDP Rolim, D Steurer & K Jansen (eds), Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018., 48, Leibniz International Proceedings in Informatics, LIPIcs, vol. 116, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 21st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2018 and the 22nd International Workshop on Randomization and Computation, RANDOM 2018, Princeton, United States, 20/08/18. https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2018.48

Improved composition theorems for functions and relations. / Koroth, Sajin; Meir, Or.
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018. ed. / Eric Blais; Jose D. P. Rolim; David Steurer; Klaus Jansen. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. 48 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 116).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Koroth, Sajin

AU - Meir, Or

PY - 2018/8/1

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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.

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SN - 9783959770859

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BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018

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Y2 - 20 August 2018 through 22 August 2018

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Koroth S, Meir O. Improved composition theorems for functions and relations. In Blais E, Rolim JDP, Steurer D, Jansen K, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 21st International Workshop, APPROX 2018, and 22nd International Workshop, RANDOM 2018. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2018. 48. (Leibniz International Proceedings in Informatics, LIPIcs). doi: 10.4230/LIPIcs.APPROX-RANDOM.2018.48

Improved composition theorems for functions and relations

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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