Checking computations in polylogarithmic time
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Fully parallelized multi prover protocols for NEXP-time (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Efficient probabilistically checkable proofs and applications to approximations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
On the power of multi-prover interactive protocols
Theoretical Computer Science
Nearly-linear size holographic proofs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Interactive proofs and the hardness of approximating cliques
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Property testing in bounded degree graphs
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
SIAM Journal on Computing
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the efficiency of local decoding procedures for error-correcting codes
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A PCP characterization of NP with optimal amortized query complexity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A Combinatorial Consistency Lemma with Application to Proving the PCP Theorem
SIAM Journal on Computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Locally Testable Codes and PCPs of Almost-Linear Length
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A Lower Bound for Testing 3-Colorability in Bounded-Degree Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Some 3CNF properties are hard to test
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Randomness-efficient low degree tests and short PCPs via epsilon-biased sets
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A Tight Characterization of NP with 3 Query PCPs
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Lower Bounds for Testing Bipartiteness in Dense Graphs
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Exponential lower bound for 2-query locally decodable codes via a quantum argument
Journal of Computer and System Sciences - Special issue: STOC 2003
Simple PCPs with poly-log rate and query complexity
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Almost Orthogonal Linear Codes are Locally Testable
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
The Complexity of Online Memory Checking
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Sub-constant error low degree test of almost-linear size
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The PCP theorem by gap amplification
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Robust locally testable codes and products of codes
Random Structures & Algorithms
SIGACT news complexity theory column 51
ACM SIGACT News
Locally testable codes and PCPs of almost-linear length
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The PCP theorem by gap amplification
Journal of the ACM (JACM)
Delegating computation: interactive proofs for muggles
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The complexity of online memory checking
Journal of the ACM (JACM)
Affine dispersers from subspace polynomials
Proceedings of the forty-first annual ACM symposium on Theory of computing
Tolerant Linearity Testing and Locally Testable Codes
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Incrementally verifiable computation or proofs of knowledge imply time/space efficiency
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Subspace polynomials and limits to list decoding of Reed-Solomon codes
IEEE Transactions on Information Theory
Short locally testable codes and proofs: a survey in two parts
Property testing
Composition of low-error 2-query PCPs using decodable PCPs
Property testing
Short locally testable codes and proofs: a survey in two parts
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Composition of low-error 2-query PCPs using decodable PCPs
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Short locally testable codes and proofs
Studies in complexity and cryptography
Bravely, moderately: a common theme in four recent works
Studies in complexity and cryptography
Characterizations of locally testable linear-and affine-invariant families
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Characterizations of locally testable linear- and affine-invariant families
Theoretical Computer Science
Constructing high order elements through subspace polynomials
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Tolerant locally testable codes
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
The tensor product of two codes is not necessarily robustly testable
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Robust local testability of tensor products of LDPC codes
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
On 2-query codeword testing with near-perfect completeness
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Delegation of computation with verification outsourcing: curious verifiers
Proceedings of the 2013 ACM symposium on Principles of distributed computing
On the concrete efficiency of probabilistically-checkable proofs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Guest column: the quantum PCP conjecture
ACM SIGACT News
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We continue the study of the trade-off between the length of PCP sand their query complexity, establishing the following main results(which refer to proofs of satisfiability of circuits of size n): 1 We present PCPs of length exp(Õ(log log n)2)•n that can be verified by making o(log logn) Boolean queries.For every ε0, we present PCPs of length exp(logε n)• n that can be verified by making a constant number of Boolean queries. In both cases, false assertions are rejected withconstant probability (which may be set to be arbitrarily close to 1). The multiplicative overhead on the length of the proof, introduced by transforming a proof into a probabilistically checkable one, is just quasi-polylogarithmic in the first case (ofquery complexity o(log logn)), and 2(log n)ε, for any ε0, in the second case (of constant query complexity). In contrast, previous results required at least 2 √logn overhead in the length, even to get query complexity 2 √log n. Our techniques include the introduction of a new variant of PCPs that we call "Robust PCPs". These new PCPs facilitate proof composition, which is a central ingredient in construction of PCP systems. (A related notion and its composition properties were discovered independently by Dinur and Reingold. ) Our main technical contribution is a construction of a "length-efficient" Robust PCP. While the new construction uses many of the standard techniques in PCPs, it does differ from previous constructions in fundamental ways, and in particular does not use the "parallelization" step of Arora et al. . The alternative approach may be of independent interest. We also obtain analogous quantitative results for locally testable codes. In addition, we introduce a relaxed notion of locally decodable codes,and present such codes mapping k information bits to code words of length κ1+ε, for any ε0.