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On Reducibility to Complex or Sparse Sets

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Nancy LynchAuthors Info & Claims

Journal of the ACM (JACM), Volume 22, Issue 3

Pages 341 - 345

https://doi.org/10.1145/321892.321895

Published: 01 July 1975 Publication History

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References

[1]

CooK, S. A. The complexity of theorem-proving procedures. Conf. Rec. Third ACM Syrup. on Theory of Computing, 1971, pp. 151-158.

Crossref

Google Scholar

[2]

KAnP, R. Reducibility among combinatorial problems. In Complexity of Computer Computations, R. E. Miller and J. W. Thatcher, Eds., Plenum Press, New York, 1972, pp. 85-103.

Google Scholar

[3]

LYNCH, N. Complexity-class encoding sets. Submitted fer publication.

Google Scholar

[4]

LYNCH, N. Helping: Several formalizations. J. Symbolic Logic (to appear).

Google Scholar

[5]

LYNch, N., MEYEn, A., AND FmcnEn, M. Relativization of the theory of computational complexity. Trans. AMS (to appear).

Google Scholar

[6]

MEYER, A. Weak monadic second order theory of successor is not elementary-recursive. Manuscript, M.I.T., Cambridge, Mass., 1972.

Crossref

Google Scholar

[7]

STOCKMEYEn, L. Ph.D. Th., Dep. of Elec. Eng., M.I.T., Cambridge, Mass., June 1974.

Google Scholar

[8]

SOLOVAY, R. Private communication.

Google Scholar

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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
Du DKo K(2014)ReferencesTheory of Computational Complexity10.1002/9781118595091.refs(458-479)Online publication date: 13-Jun-2014
https://doi.org/10.1002/9781118595091.refs
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
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Index Terms

On Reducibility to Complex or Sparse Sets
1. Mathematics of computing
  1. Discrete mathematics
2. Theory of computation
  1. Computational complexity and cryptography
    1. Problems, reductions and completeness

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Published In

Journal of the ACM Volume 22, Issue 3

July 1975

133 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321892

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 1975

Published in JACM Volume 22, Issue 3

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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
Du DKo K(2014)ReferencesTheory of Computational Complexity10.1002/9781118595091.refs(458-479)Online publication date: 13-Jun-2014
https://doi.org/10.1002/9781118595091.refs
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
Du DKo K(2013)BibliographyTheory of Computational Complexity10.1002/9781118032916.biblio(453-473)Online publication date: 6-Dec-2013
https://doi.org/10.1002/9781118032916.biblio
Hartmanis J(2011)On effective speed-up and long proofs of trivial theorems in formal theoriesRevue française d'automatique informatique recherche opérationnelle. Informatique théorique10.1051/ita/197610R10029110:R1(29-38)Online publication date: 8-Jan-2011
https://doi.org/10.1051/ita/197610R100291
Souto A(2010)Kolmogorov complexity coresProceedings of the Programs, proofs, process and 6th international conference on Computability in Europe10.5555/1876420.1876462(376-385)Online publication date: 30-Jun-2010
https://dl.acm.org/doi/10.5555/1876420.1876462
Souto A(2010)Kolmogorov Complexity CoresPrograms, Proofs, Processes10.1007/978-3-642-13962-8_42(376-385)Online publication date: 2010
https://doi.org/10.1007/978-3-642-13962-8_42
Brassard G(2006)Relativized cryptographyIEEE Transactions on Information Theory10.1109/TIT.1983.105675429:6(877-894)Online publication date: 1-Sep-2006
https://dl.acm.org/doi/10.1109/TIT.1983.1056754
Yamakami TSuzuki T(2005)Resource bounded immunity and simplicityTheoretical Computer Science10.1016/j.tcs.2005.03.055347:1-2(90-129)Online publication date: 30-Nov-2005
https://dl.acm.org/doi/10.1016/j.tcs.2005.03.055
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Sparse np-complete sets

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