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A note on the Isomorphism Conjecture and one-way functions  (Make Corrections)  
John D. Rogers



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Abstract: omputable and the subscript m stands for many-one. There is also an m-reduction from TSP to SAT so TSP p m SAT. So, in some sense, these two problems are very similar: If we can solve one efficiently, we can solve the other efficiently as well. But we are interested in a more stringent kind of similarity: What if the NP-complete languages are isomorphic? An isomorphism between languages is a polynomial-time computable reduction that is one-toone and polynomial-time invertible. A reduction f ... (Update)

Active bibliography (related documents):   More   All
0.4:   The Isomorphism Conjecture Holds and One-way Functions Exist.. - Rogers (1994)   (Correct)
0.3:   NP Might Not Be As Easy As Detecting Unique Solutions - Beigel, Buhrman, Fortnow (1997)   (Correct)
0.3:   Complete Sets and Structure in Subrecursive Classes - Buhrman, Torenvliet (1998)   (Correct)

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BibTeX entry:   (Update)

@misc{ rogers-note,
  author = "John D. Rogers",
  title = "A note on the Isomorphism Conjecture and one-way functions",
  url = "citeseer.ist.psu.edu/365585.html" }
Citations (may not include all citations):
1911   Introduction to Automata Theory (context) - Hopcroft, Ullman - 1979
356   Computers and intractability: A guide to the theory of NPcom.. (context) - Garey, Johnson - 1979
126   On isomorphism and density of NP and other complete sets (context) - Berman, Hartmanis - 1976
126   On isomorphism and density of NP and other complete sets (context) - Berman, Hartmanis - 1977
94   Complexity measures for public-key cryptosystems (context) - Grollmann, Selman - 1988
60   Generic oracles and oracle classes (context) - Blum, Impagliazzo - 1987
35   Polynomial reducibilities and complete sets (context) - Berman - 1977
32   An oracle builder's toolkit - Fenner, Fortnow et al. - 1993
26   Bulletin of the European Association for Theoretical Compute.. (context) - Fortnow, of et al. - 1994
23   The isomorphism conjecture fails relative to a random oracle - Kurtz, Mahaney et al. - 1989
20   Separability and one-way functions - Fortnow, Rogers - 1994
19   The isomorphism conjecture holds relative to an oracle - Fenner, Fortnow et al. - 1992
16   Oracles for structural properties: The isomorphism problem a.. (context) - Homer, Selman - 1992
13   NP might not be as easy as detecting unique solutions - Beigel, Buhrman et al. - 1998
12   One-way functions and the nonisomorphism of NP-complete sets (context) - Hartmanis, Hemachandra - 1991
9   The Isomorphism Conjecture holds and one-way functions exist.. - Rogers - 1997
8   A note on many-one and 1-truth table complete sets (context) - Homer, Kurtz et al. - 1993
6   A relativized failure of the Berman-Hartmanis conjecture (context) - Kurtz - 1983

Documents on the same site (http://www.depaul.edu/~jrogers/Publications/):
Inverting Onto Functions - Stephen Fenner (1996)   (Correct)
Complexity Limitations on Quantum Computation - Fortnow, Rogers (1997)   (Correct)

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