Is P versus NP formally independent

Is P versus NP formally independent (2003)

Cached

Download Links

by Lance Fortnow , Scott Aaronson

Venue:	Bulletin of the European Association for Theoretical Computer Science
Citations:	7 - 0 self

BibTeX

@ARTICLE{Fortnow03isp,
    author = {Lance Fortnow and Scott Aaronson},
    title = {Is P versus NP formally independent},
    journal = {Bulletin of the European Association for Theoretical Computer Science},
    year = {2003},
    volume = {81},
    pages = {109--136}
}

Bookmark

OpenURL

Abstract

I have moved back to the University of Chicago and so has the web page for this column. See above for new URL and contact informaion. This issue Scott Aaronson writes quite an interesting (and opinionated) column on whether the P = NP question is independent of the usual axiom systems. Enjoy!

Citations

1117	Reducability Among Combinatorial Problems - Karp - 1972
636	The complexity of theorem-proving procedures - Cook - 1971
601	A pseudorandom generator from any one-way function - H˚astad, Impagliazzo, et al. - 1999
544	How to construct random functions - Goldreich, Goldwasser, et al. - 1986
356	Nondeterministic exponential time has two-prover interactive protocols - Babai, Fortnow, et al. - 1990
262	Algebraic methods in the theory of lower bounds for Boolean circuit complexity - Smolensky - 1987
121	Number-theoretic constructions of efficient pseudorandom functions - Naor, Reingold - 1997
121	Lower bounds for the monotone complexity of some boolean functions - Razborov - 1985
120	bounds for resolution and cutting plane proofs and monotone computations - Pudlák, “Lower - 1997
118	The Fabric of Reality - Deutsch - 2000
115	circuits, and the polynomial time hierarchy - FURST, SAXE, et al.
82	Set Theory and the Continuum Hypothesis - Cohen - 1966
75	The consistency of the axiom of choice and of the generalized continuum hypothesis - Gödel - 1940
71	Every Prime has a Succinct Certificate - Pratt - 1975
67	Some consequences of cryptographic conjectures for S 1 2 and EF - Krajíček, Pudlák - 1995
64	Propositional proof complexity: Past, present, and future - Beame, Pitassi - 2001
62	Circuit-Size Lower Bounds and Non-Reducibility to Sparse Sets - Kannan - 1982
51	Unprovability of lower bounds on the circuit size in certain fragments of bounded arithmetic - Razborov - 1995
46	Positive vacuum energy and the N-bound - Bousso
46	Resolution Lower Bounds for the Weak Pigeonhole Principle. Found at Electronic Col-loqium on Computational Complexity, Reports Series 2001, Available at http://www.eccc.unitrier.de/eccc - Raz - 1983
45	Bounded arithmetic and lower bounds in boolean complexity - Razborov - 1993
40	Nonrelativizing separations - Buhrman, Fortnow, et al. - 1998
40	Resolution lower bounds for perfect matching principles - Razborov
39	Pseudorandom generators hard for k-DNF resolution and polynomial calculus resolution - Razborov - 2003
38	The history and status of the P versus NP question - Sipser - 1992
37	The intractability of resolution, Theoretical Computer Science 39 - Haken - 1985
35	Number-Theoretic Constructions of Ecient Pseudo-Random Functions - Naor, Reingold - 1997
29	Universal Search Problems”, Problemy Peredaci Informacii 9 - Levin - 1973
28	A Σ 1 1 formula on finite structures, Annals of Pure and Applied Logic 24(1983):1–49 - Ajtai
28	Geometric Complexity Theory I: An Approach to the P vs. NP and Related Problems - Mulmuley, Sohoni
26	bounds for propositional proofs and independence results in bounded arithmetic - Razborov, Lower - 1996
23	bounds on the size of bounded-depth networks over the complete basis with logical addition - Lower - 1987
19	An elementary problem equivalent to the Riemann hypothesis - Lagarias
16	On the Restricted Ordinal Theorem - Goodstein - 1944
15	Superpolynomial versus half-exponential circuit size in the exponential hierarchy - Miltersen, Vinodchandran, et al.
14	Harrington: A mathematical incompleteness - Paris, L
10	Bounded arithmetic and propositional proof complexity - Buss - 1995
10	The Continuum Hypothesis, Part I - Woodin - 2001
6	On the Independence of P versus NP - Ben-David, Halevi - 1992
6	How to prove representation-independent independence results - Kurtz, O’Donnell, et al. - 1987
6	Lenstra Jr. The Development of the Number Field Sieve - Lenstra, W - 1993
5	and 32 others (Supernova Cosmology Project). Measurements of Ω and Λ from 42 highredshift supernovae - Perlmutter - 1999
5	A logical approach to the problem "P=NP - Sazanov - 1980
4	The P=?NP poll - Gasarch - 2002
4	Independence results about context-free languages and lower bounds - Hartmanis - 1985
4	Understanding the Mulmuley-Sohoni approach to P vs - Regan
3	Bounded arithmetic, cryptography, and complexity, Theoria 63:147–167 - Buss - 1997
3	The consistency of P=NP and related problems within fragments of number theory - DeMillo, Lipton - 1979
3	Independence results in computer science - Joseph, Young - 1981
3	On the concepts of completeness and interpretation of formal systems, Fundamenta Mathematicae 39:103–127 - Kreisel - 1952