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Hard-core theorems for complexity classes

Authors:

Shimon Even,

Alan L. Selmen, and

Yacov YacobiAuthors Info & Claims

Journal of the ACM (JACM), Volume 32, Issue 1

Pages 205 - 217

https://doi.org/10.1145/2455.214111

Published: 01 January 1985 Publication History

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Abstract

Nancy Lynch proved that if a decision problem A is not solvable in polynomial time, then there exists an infinite recursive subset X of its domain on which the decision is almost everywhere complex. In this paper, general theorems of this kind that can be applied to several well-known automata-based complexity classes, including a common class of randomized algorithms, are proved.

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Stockmeyer L(2014)Classifying the computational complexity of problemsThe Journal of Symbolic Logic10.2307/227385852:1(1-43)Online publication date: 12-Mar-2014
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Shimizu AMatsuzaki YUkena A(2013)Necessity of Superposition of Macroscopically Distinct States for Quantum Computational SpeedupJournal of the Physical Society of Japan10.7566/JPSJ.82.05480182:5(054801)Online publication date: 15-May-2013
https://doi.org/10.7566/JPSJ.82.054801
Ambos-Spies KBrandt UZiegler M(2013)Real Benefit of Promises and AdviceThe Nature of Computation. Logic, Algorithms, Applications10.1007/978-3-642-39053-1_1(1-11)Online publication date: 2013
https://doi.org/10.1007/978-3-642-39053-1_1
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Index Terms

Hard-core theorems for complexity classes
1. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity classes
  2. Models of computation

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Published In

Journal of the ACM Volume 32, Issue 1

Jan. 1985

246 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/2455

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Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 January 1985

Published in JACM Volume 32, Issue 1

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Stockmeyer L(2014)Classifying the computational complexity of problemsThe Journal of Symbolic Logic10.2307/227385852:1(1-43)Online publication date: 12-Mar-2014
https://doi.org/10.2307/2273858
Shimizu AMatsuzaki YUkena A(2013)Necessity of Superposition of Macroscopically Distinct States for Quantum Computational SpeedupJournal of the Physical Society of Japan10.7566/JPSJ.82.05480182:5(054801)Online publication date: 15-May-2013
https://doi.org/10.7566/JPSJ.82.054801
Ambos-Spies KBrandt UZiegler M(2013)Real Benefit of Promises and AdviceThe Nature of Computation. Logic, Algorithms, Applications10.1007/978-3-642-39053-1_1(1-11)Online publication date: 2013
https://doi.org/10.1007/978-3-642-39053-1_1
Juedes DLutz J(2005)Completeness and weak completeness under polynomial-size circuitsSTACS 9510.1007/3-540-59042-0_59(26-37)Online publication date: 1-Jun-2005
https://doi.org/10.1007/3-540-59042-0_59
Schöning U(2005)Complexity cores and hard problem instancesAlgorithms10.1007/3-540-52921-7_72(232-240)Online publication date: 4-Jun-2005
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Schöning U(2005)Complexity cores and hard-to-prove formulasCSL '8710.1007/3-540-50241-6_43(273-280)Online publication date: 31-May-2005
https://doi.org/10.1007/3-540-50241-6_43
Ko KOrponen PSchöning UWatanabe O(2005)What is a hard instance of a computational problem?Structure in Complexity Theory10.1007/3-540-16486-3_99(197-217)Online publication date: 2-Jun-2005
https://doi.org/10.1007/3-540-16486-3_99
Juedes DLutz J(1995)The Complexity and Distribution of Hard ProblemsSIAM Journal on Computing10.1137/S009753979223813324:2(279-295)Online publication date: 1-Apr-1995
https://dl.acm.org/doi/10.1137/S0097539792238133
Orponen PKo KSchöning UWatanabe O(1994)Instance complexityJournal of the ACM10.1145/174644.17464841:1(96-121)Online publication date: 2-Jan-1994
https://dl.acm.org/doi/10.1145/174644.174648
Juedes DLutz J(1993)The complexity and distribution of hard problemsProceedings of the 1993 IEEE 34th Annual Foundations of Computer Science10.1109/SFCS.1993.366869(177-185)Online publication date: 3-Nov-1993
https://dl.acm.org/doi/10.1109/SFCS.1993.366869
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Recommendations

Complexity of Hard-Core Set Proofs

Nonuniformly hard boolean functions and uniform complexity classes

On the complexity of hard-core set constructions

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