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Reducibility, randomness, and intractibility (Abstract)

Authors:

Leonard Adleman and

Kenneth MandersAuthors Info & Claims

STOC '77: Proceedings of the ninth annual ACM symposium on Theory of computing

May 1977

Pages 151 - 163

https://doi.org/10.1145/800105.803405

Published: 04 May 1977 Publication History

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Abstract

The method of showing a problem NP-complete by polynomial reduction is one of the most elegant and productive in our theory ([ 1 ], [ 3 ]). It is a means of providing compelling evidence that a problem in NP is not in P. In this paper we will demonstrate new methods for showing this.

Our methods, based on a new notion of reducibility (gamma-reducibility) are apparently of more general applicability than that of polynomial reduction and are intended to be of practical value to researchers in the field.

We use our methods to “demonstrate” (i.e., give compelling evidence) that some natural problems in NP which are not known to be NP-complete are, nonetheless, not in P.

References

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Lipschitz, L., "A Remark on the Diophantine Problem for Addition and Division" to appear.

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Manders, K. and Adleman, L., "NP-Complete Decision Problems for Quadratic Polynomials", Proceedings 8th Annual ACM Symposium on Theory of Computing (1976), pp. 23-29.

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Cited By

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Silver A(2017)On the structure of gamma degreesLogic Colloquium '9010.1017/9781316718254.020(290-305)Online publication date: 24-Mar-2017
https://doi.org/10.1017/9781316718254.020
Hemaspaandra L(2014)Beautiful structuresACM SIGACT News10.1145/2670418.267043645:3(54-70)Online publication date: 17-Sep-2014
https://dl.acm.org/doi/10.1145/2670418.2670436
Homer SSelman A(2014)Turing and the development of computational complexityTuring's Legacy10.1017/CBO9781107338579.009(299-328)Online publication date: 5-Jun-2014
https://doi.org/10.1017/CBO9781107338579.009
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Index Terms

Reducibility, randomness, and intractibility (Abstract)
1. Mathematics of computing
  1. Probability and statistics
    1. Probabilistic algorithms
    2. Probabilistic reasoning algorithms
      1. Markov-chain Monte Carlo methods
      2. Sequential Monte Carlo methods
2. Theory of computation
  1. Computational complexity and cryptography
    1. Problems, reductions and completeness
  2. Models of computation
    1. Computability
      1. Turing machines

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Published In

STOC '77: Proceedings of the ninth annual ACM symposium on Theory of computing

May 1977

318 pages

ISBN:9781450374095

DOI:10.1145/800105

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: 04 May 1977

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STOC '77 Paper Acceptance Rate 31 of 87 submissions, 36%;

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

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Cited By

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Silver A(2017)On the structure of gamma degreesLogic Colloquium '9010.1017/9781316718254.020(290-305)Online publication date: 24-Mar-2017
https://doi.org/10.1017/9781316718254.020
Hemaspaandra L(2014)Beautiful structuresACM SIGACT News10.1145/2670418.267043645:3(54-70)Online publication date: 17-Sep-2014
https://dl.acm.org/doi/10.1145/2670418.2670436
Homer SSelman A(2014)Turing and the development of computational complexityTuring's Legacy10.1017/CBO9781107338579.009(299-328)Online publication date: 5-Jun-2014
https://doi.org/10.1017/CBO9781107338579.009
Hitchcock JPavan A(2013)Length-Increasing Reductions for PSPACE-CompletenessMathematical Foundations of Computer Science 201310.1007/978-3-642-40313-2_48(540-550)Online publication date: 2013
https://doi.org/10.1007/978-3-642-40313-2_48
Hughes APavan ARussell NSelman A(2012)A thirty year old conjecture about promise problemsProceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I10.1007/978-3-642-31594-7_40(473-484)Online publication date: 9-Jul-2012
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Arvind VKöbler JMundhenk M(2011)Monotonous and randomized reductions to sparse setsRAIRO - Theoretical Informatics and Applications10.1051/ita/199630020155130:2(155-179)Online publication date: 8-Jan-2011
https://doi.org/10.1051/ita/1996300201551
Balcázar JRusso D(2011)Immunity and simplicity in relativizations of probabilistic complexity classesRAIRO - Theoretical Informatics and Applications10.1051/ita/198822020227122:2(227-244)Online publication date: 8-Jan-2011
https://doi.org/10.1051/ita/1988220202271
Köppe M(2011)On the Complexity of Nonlinear Mixed-Integer OptimizationMixed Integer Nonlinear Programming10.1007/978-1-4614-1927-3_19(533-557)Online publication date: 15-Nov-2011
https://doi.org/10.1007/978-1-4614-1927-3_19
Dunne P(2008)The Computational Complexity of Ideal Semantics IProceedings of the 2008 conference on Computational Models of Argument: Proceedings of COMMA 200810.5555/1566134.1566149(147-158)Online publication date: 21-Jun-2008
https://dl.acm.org/doi/10.5555/1566134.1566149
Harkins RHitchcock JPavan A(2007)Strong reductions and isomorphism of complete setsProceedings of the 27th international conference on Foundations of software technology and theoretical computer science10.5555/1781794.1781810(168-178)Online publication date: 12-Dec-2007
https://dl.acm.org/doi/10.5555/1781794.1781810
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