Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
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
PCP characterizations of NP: towards a polynomially-small error-probability
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Noise stability of functions with low in.uences invariance and optimality
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Conditional hardness for approximate coloring
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
ON THE HARDNESS OF APPROXIMATING MULTICUT AND SPARSEST-CUT
Computational Complexity
Locally testable codes and PCPs of almost-linear length
Journal of the ACM (JACM)
Robust PCPs of Proximity, Shorter PCPs, and Applications to Coding
SIAM Journal on Computing
Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?
SIAM Journal on Computing
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
Optimal algorithms and inapproximability results for every CSP?
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Sub-Constant Error Low Degree Test of Almost-Linear Size
SIAM Journal on Computing
Two Query PCP with Sub-Constant Error
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
On 2-query codeword testing with near-perfect completeness
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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The Unique Games Conjecture (UGC) is an important open problem in the research of PCPs and hardness of approximation. The conjecture is a strengthening of the PCP Theorem, predicting the existence of a special type of PCP verifiers: 2-query verifiers that only make unique tests. Moreover, the UGC predicts that such PCP verifiers can have almost-perfect completeness and low-soundness. The computational complexity notion of a PCP is closely related to the combinatorial notion of a Locally Testable Code (LTC). LTCs are error-correcting codes with codeword testers that only make a constant number of queries to the tested word. All known PCP constructions use LTCs as building blocks. Furthermore, to obtain PCPs with certain properties, one usually uses LTCs with corresponding properties. In light of the strong connection between PCPs and LTCs, one may conjecture the existence of LTCs with properties similar to the ones required by the UGC. In this work we show limitations on such LTCs: We consider 2-query LTCs with codeword testers that only make unique tests. Roughly speaking, we show that any such LTC with relative distance close to 1, almost-perfect completeness and low-soundness, is of constant size. While our result does not imply anything about the correctness of the UGC, it does show some limitations of unique tests, compared, for example, to projection tests.