Probabilistically checkable proofs

Can a proof be checked without reading it?

[1]  J. Radhakrishnan,et al.  On Dinur’s proof of the PCP theorem , 2006 .

[2]  Irit Dinur,et al.  The PCP theorem by gap amplification , 2006, STOC.

[3]  Dan Suciu,et al.  Journal of the ACM , 2006 .

[4]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[5]  R. Steele,et al.  Optimization , 2005, Encyclopedia of Biometrics.

[6]  Subhash Khot Guest column: inapproximability results via Long Code based PCPs , 2005, SIGA.

[7]  Eli Ben-Sasson,et al.  Simple PCPs with poly-log rate and query complexity , 2005, STOC '05.

[8]  Carsten Lund,et al.  Non-deterministic exponential time has two-prover interactive protocols , 2005, computational complexity.

[9]  Omer Reingold,et al.  Assignment testers: towards a combinatorial proof of the PCP-theorem , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[10]  Johan Håstad,et al.  Some optimal inapproximability results , 2001, JACM.

[11]  Luca Trevisan,et al.  A PCP characterization of NP with optimal amortized query complexity , 2000, STOC '00.

[12]  Uriel Feige,et al.  Two-Prover Protocols - Low Error at Affordable Rates , 2000, SIAM J. Comput..

[13]  Lars Engebretsen,et al.  Clique Is Hard To Approximate Within , 2000 .

[14]  J. Håstad Clique is hard to approximate withinn1−ε , 1999 .

[15]  Oded Goldreich,et al.  Modern Cryptography, Probabilistic Proofs and Pseudorandomness , 1998, Algorithms and Combinatorics.

[16]  Luca Trevisan,et al.  Probabilistically checkable proofs with low amortized query complexity , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[17]  Venkatesan Guruswami,et al.  A tight characterization of NP with 3 query PCPs , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[18]  U. Feige A threshold of ln n for approximating set cover , 1998, JACM.

[19]  Luca Trevisan,et al.  Recycling queries in PCPs and in linearity tests (extended abstract) , 1998, STOC '98.

[20]  Uri Zwick,et al.  Approximation algorithms for constraint satisfaction problems involving at most three variables per constraint , 1998, SODA '98.

[21]  Sanjeev Arora,et al.  Probabilistic checking of proofs: a new characterization of NP , 1998, JACM.

[22]  Uri Zwick,et al.  A 7/8-approximation algorithm for MAX 3SAT? , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[23]  Satissed Now Consider Improved Approximation Algorithms for Maximum Cut and Satissability Problems Using Semideenite Programming , 1997 .

[24]  László Lovász,et al.  Interactive proofs and the hardness of approximating cliques , 1996, JACM.

[25]  Ronitt Rubinfeld,et al.  Robust Characterizations of Polynomials with Applications to Program Testing , 1996, SIAM J. Comput..

[26]  Phokion G. Kolaitis Hardness Of Approximations , 1996 .

[27]  D. Hochbaum Approximation Algorithms for NP-Hard Problems , 1996 .

[28]  David P. Williamson,et al.  Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming , 1995, JACM.

[29]  Mihir Bellare,et al.  Free bits, PCPs and non-approximability-towards tight results , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[30]  Ran Raz,et al.  A parallel repetition theorem , 1995, STOC '95.

[31]  William Hugh Murray,et al.  Modern Cryptography , 1995, Information Security Journal.

[32]  Lance Fortnow,et al.  On the Power of Multi-Prover Interactive Protocols , 1994, Theor. Comput. Sci..

[33]  Carsten Lund,et al.  On the hardness of approximating minimization problems , 1994, JACM.

[34]  Daniel A. Spielman,et al.  Nearly-linear size holographic proofs , 1994, STOC '94.

[35]  Mihir Bellare,et al.  Improved non-approximability results , 1994, STOC '94.

[36]  Carsten Lund,et al.  Efficient probabilistic checkable proofs and applications to approximation , 1994, STOC '94.

[37]  Jacques Stern,et al.  The hardness of approximate optima in lattices, codes, and systems of linear equations , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

[38]  Carsten Lund,et al.  Proof verification and hardness of approximation problems , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[39]  Adi Shamir,et al.  IP = PSPACE , 1992, JACM.

[40]  Silvio Micali,et al.  Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems , 1991, JACM.

[41]  Leonid A. Levin,et al.  Checking computations in polylogarithmic time , 1991, STOC '91.

[42]  Carsten Lund,et al.  Algebraic methods for interactive proof systems , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[43]  Manuel Blum,et al.  Self-testing/correcting with applications to numerical problems , 1990, STOC '90.

[44]  Joan Feigenbaum,et al.  Hiding Instances in Multioracle Queries , 1990, STACS.

[45]  Avi Wigderson,et al.  Dispersers, deterministic amplification, and weak random sources , 1989, 30th Annual Symposium on Foundations of Computer Science.

[46]  Russell Impagliazzo,et al.  How to recycle random bits , 1989, 30th Annual Symposium on Foundations of Computer Science.

[47]  A. Wigderson,et al.  Disperser graphs, deterministic amplification, and imperfect random sources (גרפים מפזרים, הגברה דטרמיניסטית ומקורות אקראים חלשים.) , 1991 .

[48]  Avi Wigderson,et al.  Multi-prover interactive proofs: how to remove intractability assumptions , 2019, STOC '88.

[49]  Mihalis Yannakakis,et al.  Optimization, approximation, and complexity classes , 1991, STOC '88.

[50]  László Babai,et al.  Arthur-Merlin Games: A Randomized Proof System, and a Hierarchy of Complexity Classes , 1988, J. Comput. Syst. Sci..

[51]  László Babai,et al.  Trading group theory for randomness , 1985, STOC '85.

[52]  Silvio Micali,et al.  The knowledge complexity of interactive proof-systems , 1985, STOC '85.

[53]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[54]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.