research-article

Correlation bounds and #SAT algorithms for small linear-size circuits

Authors:

Ruiwen Chen and

Valentine KabanetsAuthors Info & Claims

Theoretical Computer Science, Volume 654, Issue C

Pages 2 - 10

https://doi.org/10.1016/j.tcs.2016.05.005

Published: 22 November 2016 Publication History

Abstract

We revisit the gate elimination method, generalize it to prove correlation bounds of boolean circuits with Parity, and also derive deterministic satisfiability counting algorithms for small linear-size circuits. Let B2 be the full binary basis, and let U2=B2{,}. We prove that, for circuits over U2 of size 3nn for any constant >0.5, the correlation with Parity is at most 2n(1), and there is a #SAT algorithm (which counts the number of satisfying assignments) running in time 2nn(1); for circuit size 3nn for >0, the correlation with Parity is at most 2(n), and there is a #SAT algorithm running in time 2n(n). Similar correlation bounds and algorithms are also proved for circuits over B2 of size almost 2.5n.

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Cited By

Hirahara SIlango RWilliams RMohar BShinkar IO'Donnell R(2024)Beating Brute Force for Compression ProblemsProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649778(659-670)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649778
Chen LLi JYang T(2022)Extremely efficient constructions of hash functions, with applications to hardness magnification and PRFsProceedings of the 37th Computational Complexity Conference10.4230/LIPIcs.CCC.2022.23(1-37)Online publication date: 20-Jul-2022
https://dl.acm.org/doi/10.4230/LIPIcs.CCC.2022.23
Knop ALovett SMcGuire SYuan W(2021)Guest ColumnACM SIGACT News10.1145/3471469.347147952:2(46-70)Online publication date: 17-Jun-2021
https://dl.acm.org/doi/10.1145/3471469.3471479

Index Terms

Correlation bounds and #SAT algorithms for small linear-size circuits
1. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity classes
  2. Design and analysis of algorithms

Index terms have been assigned to the content through auto-classification.

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cover image Theoretical Computer Science

Theoretical Computer Science Volume 654, Issue C

November 2016

82 pages

ISSN:0304-3975

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Copyright © Elsevier B.V.

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Elsevier Science Publishers Ltd.

United Kingdom

Publication History

Published: 22 November 2016

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Cited By

Hirahara SIlango RWilliams RMohar BShinkar IO'Donnell R(2024)Beating Brute Force for Compression ProblemsProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649778(659-670)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649778
Chen LLi JYang T(2022)Extremely efficient constructions of hash functions, with applications to hardness magnification and PRFsProceedings of the 37th Computational Complexity Conference10.4230/LIPIcs.CCC.2022.23(1-37)Online publication date: 20-Jul-2022
https://dl.acm.org/doi/10.4230/LIPIcs.CCC.2022.23
Knop ALovett SMcGuire SYuan W(2021)Guest ColumnACM SIGACT News10.1145/3471469.347147952:2(46-70)Online publication date: 17-Jun-2021
https://dl.acm.org/doi/10.1145/3471469.3471479

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