Abstract
We reformulate the subject of holographic proof checking in terms of three-valued logic. In this reformulation the recursive proof checking idea of Arora and Safra gets an especially elegant form. Our approach gives a more concise and accurate treatment of the holographic proof theory, and yields easy to check proofs about holographic proofs. A consequence of our results is that for any ∈ > 0 MAX3SAT instances cannot be approximated in TIME(2n1-∈ ) within a factor which tends to 1 when n tends to infinity, unless 3SAT can be solved in TIME(2n1-∈) for some ∈ > 0.
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References
S. Arora and C. Lund, Hardness of approximations. In Approximation Algorithms for NP-hard problems, D. Hochbaum, ed. PWS Publishing, 1996.
S. Arora, C, Lund, R. Motwani, M. Sudan, and M. Szegedy, Proof verification and the intractability of approximation problems. Proceedings of the 33rd Symposium on Foundations of Computer Science, IEEE 1992.
S. Arora and S. Safra. Probabilistic checking of proofs: a new characterization of NP. To appear Journal of the ACM. Preliminary version in Proceedings of the Thirty Third Annual Symposium on the Foundations of Computer Science, IEEE, 1992.
L. Babai, L. Fortnow, and C. Lund, Non-deterministic exponential time has two-prover interactive protocols. Computational Complexity, 1:3–40, 1991.
L. Babai, L. Fortnow, L. Levin, and M. Szegedy, Checking computations in polylogarithmic time. Proceedings of the Twenty Third Annual Symposium on the Theory of Computing, ACM, 1991.
L. Babai and K. Friedl, On slightly superlinear transparent proofs. Univ. Chicago Tech. Report, CS-93-13, 1993.
U. Feige, S. Goldwasser, L. Lovász, S. Safra, and M. Szegedy, Interactive proofs and the hardness of approximating cliques. Journal of the ACM, 43(2):268–292, March 1996.
L. Fortnow, J. Rompel, and M. Sipser, On the power of multi-prover interactive protocols. Theoretical Computer Science, 134(2):545–557, November 1994.
S. Goldwasser, S. Micali, and C. Rackoff, The knowledge complexity of interactive proof-systems. SIAM J. on Computing, 18(1):186–208, February 1989.
A. Polishchuk and D. Spielman, Nearly Linear Sized Holographic Proofs. Proceedings of the Twenty Sixth Annual Symposium on the Theory of Computing, ACM, 1994.
R. Raz, A parallel repetition theorem. Proceedings of the Twenty Seventh Annual Symposium on the Theory of Computing, ACM, 1995.
M. Sudan, Efficient Checking of Polynomials and Proofs and the Hardness of Approximation Problems. Ph.D. Thesis, U.C. Berkeley, 1992. Also appears as ACM Distinguished Theses, Lecture Notes in Computer Science, no. 1001, Springer, 1996.
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Szegedy, M. (1999). Many-Valued Logics and Holographic Proofs. In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds) Automata, Languages and Programming. Lecture Notes in Computer Science, vol 1644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48523-6_64
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DOI: https://doi.org/10.1007/3-540-48523-6_64
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