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Circuits and local computation

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A. C. YaoAuthors Info & Claims

STOC '89: Proceedings of the twenty-first annual ACM symposium on Theory of computing

Pages 186 - 196

https://doi.org/10.1145/73007.73025

Published: 01 February 1989 Publication History

Abstract

This paper contains two parts. In Part I, we show that polynomial-size monotone threshold circuits of depth k form a proper hierarchy in parameter k. This implies in particular that monotone TC⁰ is properly contained in NC¹. In Part II, we introduce a new concept, called local function, which tries to characterize when a function can be efficiently computed using only localized processing elements. It serves as a unifying framework for viewing related and sometimes apparently unrelated results. In particular, it will be demonstrated that the recent results on lower bounds for monotone circuits by Razborov [Ra1] and Karchmer and Wigderson [KW], as well as a main theorem in Part I of this paper, can be regarded as proving certain functions to be nonlocal. We will also suggest an approach based on locality for attacking the conjecture that (nonmonotone) TC⁰ is properly contained in NC¹.

References

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Cited By

Feng GZhang BGu YYe HHe DWang LOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Towards revealing the mystery behind chain of thoughtProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3669222(70757-70798)Online publication date: 10-Dec-2023
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Hatami PHoza WTal ATell RSaha BServedio R(2023)Depth-𝑑 Threshold Circuits vs. Depth-(𝑑+1) AND-OR TreesProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585216(895-904)Online publication date: 2-Jun-2023
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Chen LHirahara SOliveira IPich JRajgopal NSanthanam R(2022)Beyond Natural Proofs: Hardness Magnification and LocalityJournal of the ACM10.1145/353839169:4(1-49)Online publication date: 23-Aug-2022
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Index Terms

Circuits and local computation
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Generating functions
  2. Mathematical analysis
    1. Mathematical optimization
2. Theory of computation

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cover image ACM Conferences

STOC '89: Proceedings of the twenty-first annual ACM symposium on Theory of computing

February 1989

600 pages

ISBN:0897913078

DOI:10.1145/73007

Editor:
D. S. Johnson

Copyright © 1989 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 February 1989

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STOC89: 21st Annual ACM Symposium on the Theory of Computing

May 14 - 17, 1989

Washington, Seattle, USA

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STOC '89 Paper Acceptance Rate 56 of 196 submissions, 29%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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https://dl.acm.org/doi/10.5555/3666122.3669222
Hatami PHoza WTal ATell RSaha BServedio R(2023)Depth-𝑑 Threshold Circuits vs. Depth-(𝑑+1) AND-OR TreesProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585216(895-904)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585216
Chen LHirahara SOliveira IPich JRajgopal NSanthanam R(2022)Beyond Natural Proofs: Hardness Magnification and LocalityJournal of the ACM10.1145/353839169:4(1-49)Online publication date: 23-Aug-2022
https://dl.acm.org/doi/10.1145/3538391
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Chen XOliveira IServedio RHatami HMcKenzie PKing V(2017)Addition is exponentially harder than counting for shallow monotone circuitsProceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3055399.3055425(1232-1245)Online publication date: 19-Jun-2017
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Chan SPotechin AKarloff HPitassi T(2012)Tight bounds for monotone switching networks via fourier analysisProceedings of the forty-fourth annual ACM symposium on Theory of computing10.1145/2213977.2214024(495-504)Online publication date: 19-May-2012
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Limaye NMahajan MSreenivasaiah K(2012)The Complexity of Unary Subset SumComputing and Combinatorics10.1007/978-3-642-32241-9_39(458-469)Online publication date: 2012
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Benjamini IKalai GSchramm O(2011)Noise Sensitivity of Boolean Functions and Applications to PercolationSelected Works of Oded Schramm10.1007/978-1-4419-9675-6_12(351-389)Online publication date: 1-Jul-2011
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