Multilinear formulas, maximal-partition discrepancy and mixed-sources extractors

Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

Volumn , Issue , 2008, Pages 273-282

  Raz, Ran ^a   Yehudayofft, Amir ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTERS; FIBER OPTIC CHEMICAL SENSORS; INTEGRATING CIRCUITS; LOGIC CIRCUITS; POLYNOMIAL APPROXIMATION; POLYNOMIALS; VECTORS;

ARITHMETIC CIRCUITS; COMMUNICATION COMPLEXITIES; DISJOINT SETS; LOWER BOUNDS; MULTILINEAR MODELS; NEW MODELS; RANDOM BITS;

CONTROL THEORY;

EID: 57949089733     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FOCS.2008.22     Document Type: Conference Paper

References (27)

1. S. Aaronson. Multilinear formulas and skepticism of quantum computing. In Proceedings of STOC, pages 118-127, New York, NY, USA, 2004. ACM.
2. J. Bourgain, A. A. Glibichuk, and S. V. Konyagin. Estimates for the number of sums and products and for exponential sums in fields of prime order. Journal of London Mathematical Society, 73(2):380-398, 2006.
3. B. Barak, R. Impagliazzo, and A. Wigderson. Extracting randomness using few independent sources. SIAM J. Comput., 36(4):1095-1118, 2006.
4. B. Barak, G. Kindler, R. Shaltiel, B. Sudakov, and A. Wigderson. Simulating independence: new constructions of condensers, ramsey graphs, dispersers, and extractors. In Proceedings of STOC, pages 1-10, New York, NY, USA, 2005. ACM.
5. J. Bourgain, N. Katz, and T. Tao. A sumproduct estimate in finite fields, and applications. Geometric and Functional Analysis, 14:27-57, 2004.
6. J. Bourgain. More on the sum-product phenomenon in prime fields and its applications. International Journal of Number Theory, 1:1-32, 2005.
7. J. Bourgain. On the construction of affine extractors. Geometric and Functional Analysis, 17:33-57, 2007.
8. B. Barak, A. Rao, R. Shaltiel, and A. Wigderson. 2-source dispersers for sub-polynomial entropy and ramsey graphs beating the franklwilson construction. In Proceedings of STOC, pages 671-680, New York, NY, USA, 2006. ACM.
9. B. Chor and O. Goldreich. Unbiased bits from sources of weak randomness and probabilistic communication complexity. SIAM J. Comput., 17(2):230-261, 1988.
10. M. Jerrum and M. Snir. Some exact complexity results for straight-line computations over semirings. J. ACM, 29(3):874-897, 1982.
11. S. Jukna. On the p versus np intersected with co-np question in communication complexity. Inf. Process. Lett., 96(6):202-206, 2005.
12. N. Nisan and A. Wigderson. Lower bound on arithmetic circuits via partial derivatives. Computational Complexity, 6:217-234, 1996.
13. A. Rao. Extractors for a constant number of polynomially small min-entropy independent sources. In Proceedings of STOC, pages 497-506, New York, NY, USA, 2006. ACM.
14. R. Raz. Multi-linear formulas for permanent and determinant are of super-polynomial size. In Proceedings of STOC, pages 633-641, New York, NY, USA, 2004. ACM.
15. R. Raz. Extractors with weak random seeds. In Proceedings of STOC, pages 11-20, New York, NY, USA, 2005. ACM.
16. R. Raz. Separation of multilinear circuit and formula size. Theory of Computing, 2(1):121-135, 2006.
17. R. Raz, A. Shpilka, and A. Yehudayoff. A lower bound for the size of syntactically multilinear arithmetic circuits. In Proceedings of FOCS, pages 438-448, Washington, DC, USA, 2007. IEEE Computer Society.
18. R. Raz and A. Yehudayoff. Balancing syntactically multilinear arithmetic circuits. Computational Complexity - to appear, 2008.
19. C. P. Schnorr. A lower bound on the number of additions in monotone computations. Theor. Comput. Sci., 2:305-315, 1976.
20. M. Snir. On the size complexity of monotone formulas. In Proceedings of the 7th Colloquium on Automata, Languages and Programming, pages 621-631, London, UK, 1980. Springer-Verlag.
21. E. Shamir and M. Snir. On the depth complexity of formulas. Journal Theory of Computing Systems, 13(1):301-322, 1979.
22. R. Sengupta and H. Venkateswaran. A lower bound for monotone arithmetic circuits computing 0-1 permanent. Theor. Comput. Sci., 209(1-2):389-398, 1998.
23. P. Tiwari and M. Tompa. A direct version of shamir and snir's lower bounds on monotone circuit depth. Inf. Process. Lett., 49(5):243-248, 1994.
24. L. G. Valiant. Negation can be exponentially powerful. In Proceedings of STOC, pages 189-196, New York, NY, USA, 1979. ACM.
25. U. V. Vazirani. Towards a strong communication complexity theory or generating quasirandom sequences from two communicating slightly-random sources. In Proceedings of STOC, pages 366-378, New York, NY, USA, 1985. ACM.
26. L. G. Valiant, S. Skyum, S. Berkowitz, and C. Rackoff. Fast parallel computation of polynomials using few processors. SIAM J. Comput., 12(4):641-644, 1983.
27. A. C.-C. Yao. Some complexity questions related to distributive computing (preliminary report). In Proceedings of STOC, pages 209-213, New York, NY, USA, 1979. ACM.