Supplemental Material
- Agrawal, M. Proving lower bounds via pseudo-random generators. In Proceedings of the FSTTCS (2005), Springer-Verlag, Berlin, Germany, 92--105. Google ScholarDigital Library
- Appel, K., Haken, W., Koch, J. Every planar map is four colourable. Illinois J. Math. 21 (1977), 439--567.Google Scholar
- Arora, S., Barak, B. Computation Complexity: a Modern Approach, Cambridge University Press, Cambridge, England, 2009. Google ScholarDigital Library
- Blasiak, J., Mulmuley, K., Sohoni, M. Geometric complexity theory IV: nonstandard quantum group for the Kronecker problem. cs. ArXiv preprint cs. CC/0703110 (2011).Google Scholar
- Boppana, R., Sipser, M. The complexity of finite functions. Handbook of Theoretical Computer Science. J. van Leeuwen, ed. Volume A, MIT press, 1990, 757--804. Google ScholarDigital Library
- Bürgisser, P., Clausen, M., Shokrollahi, M. Algebraic Complexity Theory, Springer-Verlag, 1997. Google ScholarCross Ref
- Bürgisser, P. and Ikenmeyer, C. Geometric complexity theory and tensor rank. arXiv:1011.1350v1 (2010).Google Scholar
- Bürgisser, P., Landsberg, J., Manivel, L., Weyman, J. An overview of mathematical issues arising in the geometric complexity theory approach to VP ≠ VNP. arXiv:0907.2850v1 {cs.CC} (2009).Google Scholar
- Cook, S. The complexity of theorem-proving procedures. In Proceedings of the third annual ACM Symposium on Theory of Computing (1971), ACM, New York, NY, 151--158. Google ScholarDigital Library
- Deligne, P. La conjecture de weil II. Publ. Math. Inst. Hau. Étud. Sci. 52 (1980), 137--252.Google Scholar
- Fortnow, L. The status of the P versus NP problem. CACM 52, 9 (2009), 78--86. Google ScholarDigital Library
- Kabanets, V., Impagliazzo, R. Derandomizing polynomial identity tests means proving circuit lower bounds. Comput. Complex. 13 (2004), 1--46. Google ScholarDigital Library
- Karp, R. Reducibility among combinatorial problems. Complexity of Computer Computations. R. Miller and J. Thatcher, eds. Plenum Press, New York, 1972, 85--103.Google Scholar
- Landsberg, J., Manivel, L., Ressayre, N. Hypersurfaces with degenerate duals and the geometric complexity theory program. arXiv:1004.4802v1 {math.AG} (2010).Google Scholar
- Levin, L. Universal sequential search problems. Probl. Inform. transm. 9 (1973), 115--116.Google Scholar
- Mignon, T., Ressayre, N. A quadratic bound for the determinant and permanent problem. Int. Math. Res. Not. 79 (2004), 4241--4253.Google ScholarCross Ref
- Mulmuley, K. Geometric Complexity Theory IX. Technical report, under preparation.Google Scholar
- Mulmuley, K. Lower bounds in a parallel model without bit operations. SIAM J. Comput. 28, 4 (1999), 1460--1509. Google ScholarDigital Library
- Mulmuley, K. Geometric Complexity Theory VII: Nonstandard Quantum Group for the Plethysm Problem. Technical Report TR-2007-14, Computer Science Department, The University of Chicago, 2007.Google Scholar
- Mulmuley, K. Geometric Complexity Theory VIII: On Canonical Bases for the Nonstandard Quantum Groups. Technical Report TR 2007-15, Computer Science Department, The University of Chicago, 2007.Google Scholar
- Mulmuley, K. Explicit proofs and the flip. arXiv:1009.0246 v1 {cs.CC} (2010).Google Scholar
- Mulmuley, K. Geometric Complexity Theory VI: The Flip via Positivity. Technical report, The Computer Science Department, The University of Chicago, 2010.Google Scholar
- Mulmuley, K. On P vs. NP and geometric complexity theory. JACM 58, 2 (2011). Google ScholarDigital Library
- Mulmuley, K., Narayanan, H., Sohoni, M. Geometric complexity theory III: on deciding nonvanishing of a Littlewood-Richardson coefficient. J. Algebr. Combinator. (Nov. 2011), 1--8. Google ScholarDigital Library
- Mulmuley, K., Sohoni, M. Geometric complexity theory I: an approach to the P vs. NP and related problems. SIAM J. Comput. 31, 2 (2001), 496--526. Google ScholarDigital Library
- Mulmuley, K., Sohoni, M. Geometric complexity theory II: towards explicit obstructions for embeddings among class varieties. SIAM J. Comput. 38, 3 (2008), 1175--1206. Google ScholarDigital Library
- Razborov, A. Lower bounds on the monotone complexity of some Boolean functions. Dokl. Akad. Nauk SSSR 281 (1985), 798--801.Google Scholar
- Strassen, V. Rank and optimal computation of generic tensors. Lin. Algebra Appl. 53 (1983), 645--685.Google ScholarCross Ref
- Valiant, L. The complexity of computing the permanent. TCS 8 (1979), 189--201.Google ScholarCross Ref
- Weyl, H. Classical Groups, Princeton University Press, Princeton, NJ, 1946.Google Scholar
Index Terms
- The GCT program toward the P vs. NP problem
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