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Probabilistic computation and linear time

Authors:

L. Fortnow,

M. SipserAuthors Info & Claims

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

Pages 148 - 156

https://doi.org/10.1145/73007.73021

Published: 01 February 1989 Publication History

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Abstract

In this paper, we give an oracle under which BPP is equal to probabilistic linear time, an unusual collapse of a complexity time hierarchy. In addition, we also give oracles where Δ^P₂ is contained in probabilistic linear time and where BPP has linear sized circuits, as well as oracles for the negation of these questions. This indicates that these questions will not be solved by techniques that relativize. Finally, we note that probabilistic linear time can not contain both NP and BPP, implying that there are languages solvable by interactive proof systems that can not be solved in probabilistic linear time.

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Cited By

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van Melkebeek DPervyshev K(2006)A Generic Time Hierarchy for Semantic Models with One Bit of AdviceProceedings of the 21st Annual IEEE Conference on Computational Complexity10.1109/CCC.2006.7(129-144)Online publication date: 16-Jul-2006
https://dl.acm.org/doi/10.1109/CCC.2006.7
Karpinski MVerbeek R(2005)On randomized versus deterministic computationAutomata, Languages and Programming10.1007/3-540-56939-1_75(227-240)Online publication date: 28-May-2005
https://doi.org/10.1007/3-540-56939-1_75
Allender EBeigel RHertrampf UHomer S(2005)A note on the almost-everywhere hierarchy for nondeterministic timeSTACS 9010.1007/3-540-52282-4_27(1-11)Online publication date: 6-Jun-2005
https://doi.org/10.1007/3-540-52282-4_27
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Index Terms

Probabilistic computation and linear time
1. Mathematics of computing
  1. Probability and statistics
2. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity classes
  2. Logic

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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

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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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 February 1989

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STOC89

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SIGACT

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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Cited By

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van Melkebeek DPervyshev K(2006)A Generic Time Hierarchy for Semantic Models with One Bit of AdviceProceedings of the 21st Annual IEEE Conference on Computational Complexity10.1109/CCC.2006.7(129-144)Online publication date: 16-Jul-2006
https://dl.acm.org/doi/10.1109/CCC.2006.7
Karpinski MVerbeek R(2005)On randomized versus deterministic computationAutomata, Languages and Programming10.1007/3-540-56939-1_75(227-240)Online publication date: 28-May-2005
https://doi.org/10.1007/3-540-56939-1_75
Allender EBeigel RHertrampf UHomer S(2005)A note on the almost-everywhere hierarchy for nondeterministic timeSTACS 9010.1007/3-540-52282-4_27(1-11)Online publication date: 6-Jun-2005
https://doi.org/10.1007/3-540-52282-4_27
Fortnow LSanthanam R(2004)Hierarchy Theorems for Probabilistic Polynomial TimeProceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science10.1109/FOCS.2004.33(316-324)Online publication date: 17-Oct-2004
https://dl.acm.org/doi/10.1109/FOCS.2004.33
Rettinger RVerbeek R(2001)Monte-Carlo Polynomial versus Linear Time - The Truth-Table CaseFundamentals of Computation Theory10.1007/3-540-44669-9_30(311-322)Online publication date: 2-Aug-2001
https://doi.org/10.1007/3-540-44669-9_30
Cai JNerurkar ASivakumar DVitter JLarmore LLeighton T(1999)Hardness and hierarchy theorems for probabilistic quasi-polynomial timeProceedings of the thirty-first annual ACM symposium on Theory of Computing10.1145/301250.301444(726-735)Online publication date: 1-May-1999
https://dl.acm.org/doi/10.1145/301250.301444
Regan KSivakumar D(1998)Probabilistic martingales and BPTIME classesProceedings. Thirteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat. No.98CB36247)10.1109/CCC.1998.694604(186-200)Online publication date: 1998
https://doi.org/10.1109/CCC.1998.694604
Fortnow LSipser MLeighton FShor P(1997)Retraction of probabilistic computation and linear timeProceedings of the twenty-ninth annual ACM symposium on Theory of computing10.1145/258533.258677Online publication date: 4-May-1997
https://dl.acm.org/doi/10.1145/258533.258677
Hemaspaandra LRamachandran AZimand M(1995)Worlds to die forACM SIGACT News10.1145/219817.21982226:4(5-15)Online publication date: 1-Dec-1995
https://dl.acm.org/doi/10.1145/219817.219822
Hemachandra LJain SVereshchagin N(1992)Banishing robust Turing completenessLogical Foundations of Computer Science — Tver '9210.1007/BFb0023873(186-197)Online publication date: 1992
https://doi.org/10.1007/BFb0023873
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