Trading group theory for randomness
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Multi-prover interactive proofs: how to remove intractability assumptions
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Algebraic methods for interactive proof systems
Journal of the ACM (JACM)
Journal of the ACM (JACM)
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
Probabilistic checking of proofs and hardness of approximation problems
Probabilistic checking of proofs and hardness of approximation problems
Impossibility results for recycling random bits in two-prover proof systems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
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)
Tiny families of functions with random properties: a quality-size trade-off for hashing
Proceedings of the workshop on Randomized algorithms and computation
SIAM Journal on Computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Boolean functions whose Fourier transform is concentrated on the first two levels
Advances in Applied Mathematics
Locally Testable Codes and PCPs of Almost-Linear Length
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A Combinatorial Consistency Lemma with Application to Proving the PCP Theorem
RANDOM '97 Proceedings of the International Workshop on Randomization and Approximation Techniques in Computer Science
Randomness-efficient low degree tests and short PCPs via epsilon-biased sets
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Robust pcps of proximity, shorter pcps and applications to coding
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Assignment Testers: Towards a Combinatorial Proof of the PCP-Theorem
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Undirected ST-connectivity in log-space
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Gap amplification in PCPs using lazy random walks
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
IEEE Transactions on Information Theory - Part 1
Delegating computation: interactive proofs for muggles
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Infeasibility of instance compression and succinct PCPs for NP
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Undirected connectivity in log-space
Journal of the ACM (JACM)
PCPs with small soundness error
ACM SIGACT News
3-bit dictator testing: 1 vs. 5/8
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
New direct-product testers and 2-query PCPs
Proceedings of the forty-first annual ACM symposium on Theory of computing
On proximity oblivious testing
Proceedings of the forty-first annual ACM symposium on Theory of computing
The detectability lemma and quantum gap amplification
Proceedings of the forty-first annual ACM symposium on Theory of computing
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Hard constraint satisfaction problems have hard gaps at location 1
Theoretical Computer Science
ACM Transactions on Computation Theory (TOCT)
Short PCPPs verifiable in polylogarithmic time with O(1) queries
Annals of Mathematics and Artificial Intelligence
Two-query PCP with subconstant error
Journal of the ACM (JACM)
Sub-linear zero-knowledge argument for correctness of a shuffle
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses
Proceedings of the forty-second ACM symposium on Theory of computing
Routing for energy minimization in the speed scaling model
INFOCOM'10 Proceedings of the 29th conference on Information communications
Data stream algorithms for codeword testing
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Other complexity classes and measures
Algorithms and theory of computation handbook
Low rate is insufficient for local testability
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Locally testable vs. locally decodable codes
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Infeasibility of instance compression and succinct PCPs for NP
Journal of Computer and System Sciences
On the Compressibility of $\mathcal{NP}$ Instances and Cryptographic Applications
SIAM Journal on Computing
Locally Testable Codes Require Redundant Testers
SIAM Journal on Computing
Theoretical Computer Science
Limitation on the rate of families of locally testable codes
Property testing
Property testing of massively parametrized problems – a survey
Property testing
Symmetric LDPC codes and local testing
Property testing
Limitation on the rate of families of locally testable codes
Property testing
Property testing of massively parametrized problems – a survey
Property testing
Symmetric LDPC codes and local testing
Property testing
Pattern Recognition and Image Analysis
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Short locally testable codes and proofs
Studies in complexity and cryptography
Limits on the rate of locally testable affine-invariant codes
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Dense locally testable codes cannot have constant rate and distance
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Efficient probabilistically checkable debates
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Almost transparent short proofs for NPR
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
On Proximity-Oblivious Testing
SIAM Journal on Computing
On the rectangle method in proofs of robustness of tensor products
Information Processing Letters
The interval constrained 3-coloring problem
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Subsampling mathematical relaxations and average-case complexity
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The tensor product of two good codes is not necessarily robustly testable
Information Processing Letters
Guest column: algebraic construction of projection PCPs
ACM SIGACT News
Efficient zero-knowledge arguments from two-tiered homomorphic commitments
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
A note about a partial no-go theorem for quantum PCP
Quantum Information & Computation
On QMA protocols with two short quantum proofs
Quantum Information & Computation
Secure two-party computation with low communication
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Survey: A survey on the structure of approximation classes
Computer Science Review
Survey: Colouring, constraint satisfaction, and complexity
Computer Science Review
Pattern Recognition and Image Analysis
SIAM Journal on Discrete Mathematics
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Taking proof-based verified computation a few steps closer to practicality
Security'12 Proceedings of the 21st USENIX conference on Security symposium
Resolving the conflict between generality and plausibility in verified computation
Proceedings of the 8th ACM European Conference on Computer Systems
Trivial low energy states for commuting Hamiltonians, and the quantum PCP conjecture
Quantum Information & Computation
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
Product-state approximations to quantum ground states
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Guest column: the quantum PCP conjecture
ACM SIGACT News
Robust Satisfiability for CSPs: Hardness and Algorithmic Results
ACM Transactions on Computation Theory (TOCT)
Locally testable codes and cayley graphs
Proceedings of the 5th conference on Innovations in theoretical computer science
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The PCP theorem [Arora and Safra 1998; Arora et. al. 1998] says that every language in NP has a witness format that can be checked probabilistically by reading only a constant number of bits from the proof. The celebrated equivalence of this theorem and inapproximability of certain optimization problems, due to Feige et al. [1996], has placed the PCP theorem at the heart of the area of inapproximability. In this work, we present a new proof of the PCP theorem that draws on this equivalence. We give a combinatorial proof for the NP-hardness of approximating a certain constraint satisfaction problem, which can then be reinterpreted to yield the PCP theorem. Our approach is to consider the unsat value of a constraint system, which is the smallest fraction of unsatisfied constraints, ranging over all possible assignments for the underlying variables. We describe a new combinatorial amplification transformation that doubles the unsat-value of a constraint-system, with only a linear blowup in the size of the system. The amplification step causes an increase in alphabet-size that is corrected by a (standard) PCP composition step. Iterative application of these two steps yields a proof for the PCP theorem. The amplification lemma relies on a new notion of “graph powering” that can be applied to systems of binary constraints. This powering amplifies the unsat-value of a constraint system provided that the underlying graph structure is an expander. We also extend our amplification lemma towards construction of assignment testers (alternatively, PCPs of Proximity) which are slightly stronger objects than PCPs. We then construct PCPs and locally-testable codes whose length is linear up to a polylog factor, and whose correctness can be probabilistically verified by making a constant number of queries. Namely, we prove SAT ∈ PCP 1/2,1[log2(n⋅poly log n), O(1)].