Checking computations in polylogarithmic time
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
A note on efficient zero-knowledge proofs and arguments (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Nearly-linear size holographic proofs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
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
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
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
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
Some optimal inapproximability results
Journal of the ACM (JACM)
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
SIAM Journal on 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
Fast approximate probabilistically checkable proofs
Information and Computation
Exponential lower bound for 2-query locally decodable codes via a quantum argument
Journal of Computer and System Sciences - Special issue: STOC 2003
Some 3CNF Properties Are Hard to Test
SIAM Journal on Computing
Approximation Algorithms for Unique Games
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Gowers uniformity, influence of variables, and PCPs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Near-optimal algorithms for unique games
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A 3-Query Non-Adaptive PCP with Perfect Completeness
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Locally testable codes and PCPs of almost-linear length
Journal of the ACM (JACM)
Tolerant property testing and distance approximation
Journal of Computer and System Sciences
The PCP theorem by gap amplification
Journal of the ACM (JACM)
Robust PCPs of Proximity, Shorter PCPs, and Applications to Coding
SIAM Journal on Computing
Assignment Testers: Towards a Combinatorial Proof of the PCP Theorem
SIAM Journal on Computing
Sub-Constant Error Low Degree Test of Almost-Linear Size
SIAM Journal on Computing
Short PCPs with Polylog Query Complexity
SIAM Journal on Computing
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
More efficient queries in PCPs for NP and improved approximation hardness of maximum CSP
Random Structures & Algorithms
Two Query PCP with Sub-Constant Error
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
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
Linearity testing in characteristic two
IEEE Transactions on Information Theory - Part 1
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
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We initiate the study of the trade-off between the length of a probabilistically checkable proof of proximity (PCPP) and the maximal soundness that can be guaranteed by a 3-query verifier with oracle access to the proof. Our main observation is that a verifier limited to querying a short proof cannot obtain the same soundness as that obtained by a verifier querying a long proof. Moreover, we quantify the soundness deficiency as a function of the proof-length and show that any verifier obtaining “best possible” soundness must query an exponentially long proof. In terms of techniques, we focus on the special class of inspective verifiers that read at most 2 proof-bits per invocation. For such verifiers, we prove exponential length-soundness trade-offs that are later on used to imply our main results for the case of general (i.e., not necessarily inspective) verifiers. To prove the exponential trade-off for inspective verifiers, we show a connection between PCPP proof length and property-testing query complexity that may be of independent interest. The connection is that any linear property that can be verified with proofs of length ℓ by linear inspective verifiers must be testable with query complexity ≈ logℓ.