ABSTRACT We review some of the known results about the complexity of computing solutions or proofs of membership for problems in NP. Trying to capture the complexity of this problem, we consider the classes of functions FP
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227
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Nondeterministic space is closed under complementation
– Immerman
- 1988
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197
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Some connections between nonuniform and uniform complexity classes
– KARP, LIPTON
- 1980
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196
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A taxonomy of problems with fast parallel algorithms
– COOK
- 1985
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190
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The complexity of optimization problems
– Krentel
- 1988
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173
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V.V.: NP is as easy as detecting unique solutions
– Valiant, Vazirani
- 1986
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101
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The method of forced enumeration for nondeterministic automata
– Szelepcsényi
- 1988
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94
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An efficient approximation scheme for the one-dimensional bin-packing problem
– Karmarkar, Karp
- 1982
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91
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A taxonomy on complexity classes of functions
– Selman
- 1994
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85
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P-selective sets, tally languages, and the behavior of polynomial-time reducibilities on NP
– Selman
- 1979
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81
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The complexity of promise problems with applications to public-key cryptography
– Even, Selman, et al.
- 1984
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78
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Qualitative relativizations of complexity classes
– Book, Long, et al.
- 1985
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73
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Some connections between bounded query classes and non-uniform complexity
– Amir, Beigel, et al.
- 1990
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60
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On limited nondeterminism and the complexity of the V-C dimension
– Papadimitriou, Yannakakis
- 1996
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56
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A very hard log-space counting class
– Alvarez, Jenner
- 1993
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48
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Approximable sets
– Beigel, Kummer, et al.
- 1995
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48
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The complexity of iterated multiplication
– Immerman, Landau
- 1995
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46
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On self-reducibility and weak P-selectivity
– Ko
- 1983
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42
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On polynomial-time truth-table reducibilities of intractable sets to P-selective sets
– Toda
- 1991
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39
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Computing solutions uniquely collapses the polynomial hierarchy
– Hemaspaandra, Naik, et al.
- 1996
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35
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Computing functions with parallel queries to NP
– Jenner, Toran
- 1995
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25
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PP is as hard as the polynomial time hierarchy
– Toda
- 1991
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23
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On bounded queries and approximation
– Chang, Gasarch, et al.
- 1997
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21
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Oracles that compute values
– Fenner, Homer, et al.
- 1997
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21
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On the non-uniform complexity of the graph isomorphism problem
– Lozano, Torán
- 1992
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20
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Self-witnessing polynomial-time complexity and prime factorization
– Fellows, Koblitz
- 1992
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16
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Classes of bounded nondeterminism
– D'iaz, Tor'an
- 1990
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15
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On the query complexity of clique size and maximum satisfiability
– Chang
- 1994
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15
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Functions computable with limited access to NP
– Ogihara
- 1996
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14
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Functions computable with nonadaptive queries to NP
– Buhrman, Kadin, et al.
- 1998
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13
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The complexity of finding middle elements
– Vollmer, Wagner
- 1993
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13
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Structural analysis of the complexity of inverse functions
– Watanabe, Toda
- 1993
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12
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The complexity of computing maximal word functions
– Allender, Bruschi, et al.
- 1993
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12
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NP-hard sets are P-superterse unless R=NP
– Beigel
- 1988
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11
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OptP-completeness as the normal behavior of NP-complete problems
– Gasarch, Krentel, et al.
- 1995
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7
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The complexity of generating and checking proofs of membership
– Buhrman, Thierauf
- 1996
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7
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The complexity of finding medians
– Toda
- 1990
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6
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Refining nondeterminism in relativized complexity classes
– Kintala, Fischer
- 1984
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6
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Two characterizations of the logarithmic alternation hierarchy
– Lange
- 1986
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5
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On problems with short certificates
– Farr
- 1994
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4
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Adaptive logspace reducibility and parallel time
– Alvarez, Jenner
- 1995
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3
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On finding a minimum dominating set in a tournament
– Megiddo, Vishkin
- 1988
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2
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A note on logspace optimization
– Àlvarez, Jenner
- 1995
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2
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A note on p-selective sets and on adaptive versus nonadaptive queries to NP
– Cai, Naik, et al.
- 1994
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1
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A note on decision vs. search for graph automorphism
– Agrawal, Arvind
- 1996
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1
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Counting complexity. Chapter 4, this volume
– Fortnow
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1
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The Graph Isomorphism problem is low for PP
– Kobler, Schoning, et al.
- 1992
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1
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New consequences of NP having small circuits
– Kobler, Watanabe
- 1995
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1
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Solutions for the Group Intersection Problem can be obtained with parallel queries
– Tor'an
- 1995
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