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STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
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STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
When Hamming meets Euclid: the approximability of geometric TSP and MST (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Property testing in bounded degree graphs
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Improved low-degree testing and its applications
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SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
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Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
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CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
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AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
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Studies in complexity and cryptography
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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The first part of this paper presents new proof systems and improved non-approximability results. In particular we present a proof system for NP using logarithmic randomness and two amortized free bits, so that Max clique is hard within N/sup 1/3/ and chromatic number within N/sup 1/5/. We also show hardness of 38/37 for Max-3-SAT, 27/26 for vertex cover, 82/81 for Max-cut, and 94/93 for Max-2-SAT. The second part of this paper presents a "reverse" of the FGLSS connection by showing that an NP-hardness result for the approximation of Max clique to within a factor of N/sup 1/(g+1/) would imply a probabilistic verifier for NP with logarithmic randomness and amortized free-bit complexity g. We also show that "existing techniques" won't yield proof systems of less than two bits in amortized free bit complexity. Finally, we initiate a comprehensive study of PCP and FPCP parameters, proving several triviality results and providing several useful transformations.