Elusive functions and lower bounds for arithmetic circuits

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2008, Pages 711-720

  Raz, Ran ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

Theory

Indexed keywords

LINEAR ALGEBRA; LOGIC CIRCUITS; MAPPING; POLYNOMIAL APPROXIMATION; TIMING CIRCUITS;

AFFINE SUBSPACES; ARITHMETIC CIRCUIT; CONSTANT DEGREE; EXPLICIT CONSTRUCTIONS; POLYNOMIAL CURVE; POLYNOMIAL MAPPINGS; SUPER-POLYNOMIALS; THEORY;

COMPUTATION THEORY;

EID: 57049112766     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1374376.1374479     Document Type: Conference Paper

References (36)

1. 1 -Formulae on Finite Structures. Ann. Pure Appl. Logic 24: 1-48 (1983)
2. M. Alekhnovieh, E. Ben-Sasson, A. Razborov, A. Wigderson. Pseudorandom Generators in Propositional Proof Complexity. SIAM J. Comput. 34(1): 67-88 (2004) (preliminary version in FOCS 2000)
3. M. Alekhnovieh, A. Razborov. Lower Bounds for the Polynomial Calculus: Non-Binomial Case. Proceedings of the Steklov Institute of Mathematics. 242: 18-35 (2003) (preliminary version in FOCS 2001)
4. P. Burgisser. Completeness and. Reduction in Algebraic Complexity Theory. Springer-Verlag Berlin, (2000)
5. P. Burgisser, M. Clausen, M. A. Shokrollahi. Algebraic Complexity Theory. Springer-Verlag Berlin, (1997)
6. W. Baur, V. Strassen. The Complexity of Partial Derivatives. Theor. Comput. Sci. 22: 317-330 (1983)
7. D. Dolev, C. Dwork, N. Pippenger, A. Wigderson. Superconcentrators, Generalizers and Generalized Connectors with Limited Depth. STOC 1983: 42-51
8. M. L. Furst, J. B. Saxe, M. Sipser. Parity, Circuits, and the Polynomial-Time Hierarchy. Mathematical Systems Theory 17(1): 13-27 (1984) (preliminary version in FOCS 1981)
9. J. von zur Gathen. Feasible Arithmetic Computations: Valiant's Hypothesis. J. Symbolic Computation 4(2): 137-172 (1987)
10. J. von zur Gathen. Algebraic Complexity Theory. Ann. B.ev. Computer Science 3: 317-347 (1988)
11. D. Grigoriev, M. Karpinski. An Exponential Lower Bound for Depth 3 Arithmetic Circuits. STOC 1998: 577-582
12. D. Grigoriev, A. A. Razborov. Exponential Lower Bounds for Depth 3 Arithmetic Circuits in Algebras of Functions over Finite Fields. Applicable. Algebra in Engineering, Communication and Computing 10(6): 465-487 (2000) (preliminary version in FOCS 1998)
13. J. Hastad. Almost Optimal Lower Bounds for Small Depth Circuits, Advances in Computing Research 5: 143-170 (1989) (preliminary version in STOC 1986)
14. R. Impagliazzo, V. Kabanets. Derandomizing Polynomial Identity Tests Means Proving Circuit Lower Bounds. Computational Complexity 13(1-2): 1-46 (2004) (preliminary version in STOC 2003)
15. R. J. Lipton. Polynomials with 0-1 Coefficients that Are Hard to Evaluate. SIAM J. Comput. 7(1): 61-69 (1978) (preliminary version in FOCS 1975)
16. S.V. Lokam. Spectral Methods for Matrix Rigidity with Applications to Size-Depth Tradeoffs and Communication Complexity. Journal of Computer and System Sciences (2001) (preliminary version in FOCS 1995)
17. N. Nisan, Lower Bounds for Non-Commutative Computation. STOC 1991: 410-418
18. N. Nissan, A. Wigderson. On the Complexity of Bilinear Forms. STOC 1995: 723-732
19. P. Pudlak. Communication in Bounded Depth Circuits. Combinatorial 14(2): 203-216 (1994)
20. P. Pudlak. A Note on Using the Detrminant for Proving Lower Bounds on the Size of Linear Circuits. Electronic Colloquium on Computational Complexity (ECCC), Report No. 42, 1998.
21. R. Raz. On the Complexity of Matrix Product. SIAMJ. Comput. 32(5) (2003) (preliminary version in STOC 2002)
22. R. Raz. Multi-Linear Formulas for Permanent and Determinant are of Super-Polynomial Size. STOC 2004: 633-641
23. 2)
24. A. A. Razborov. Lower Bounds on the Size of Bounded-Depth Networks over a Complete Basis with Logical Addition (in Russian). Matematicheskie Zametki, 41(4): 598-607 (1987).
25. English translation in Mathematical Notes of the Academy of Sci. of the USSB. 41(4): 333-338, 1987
26. A. A. Razborov. Bounded Arithmetic and Lower-Bounds in Boolean Complexity. Feasible Mathematics II. Progress in Computer Science and Applied Logic, 13: 344-386 (1995)
27. R., Raz, A. Shpilka. Lower Bounds for Matrix Product in Bounded Depth Circuits with Arbitrary Gates. SIAM J. Comput. 32(2): 488-513 (2003) (preliminary version in STOC 2001)
28. R., Raz, A. Yehudayoff. Multilinear Formulas, Maximal-Partition Discrepancy and Mixed-Sources Extractors. Manuscript, 2007.
29. R., Smolensky. Algebraic Methods in the Theory of Lower Bounds for Boolean Circuit Complexity STOC 1987: 77-82
30. V. Strassen. Polynomials with Rational Coefficients Which Are Hard to Compute. SIAM J. Comput. 3(2): 128-149 (1974)
31. V. Strassen. Die Berechnungskomplexität der Symbolischen Differentiation von Interpolationspolynomen. Theor. Comput. Sci. 1(1): 21-25 (1975)
32. V. Shoup, R. Smolensky. Lower Bounds for Polynomial Evaluation and Interpolation Problems FOCS 1991: 378-383
33. A. Shpilka, A. Wigderson. Depth-3 Arithmetic Circuits Over Fields of Characteristic Zero. Computational Complexity 10(1): 1-27 (2001) (preliminary version in Conference on Computational Complexity 1999)
34. L. G. Valiant. Completeness Classes in Algebra STOC 1979: 249-261
35. L. G. Valiant, S. Skyum, S. Berkowitz, C. Rackoff. Fast Parallel Computation of Polynomials Using Few Processors. SIAM J. Comput. 12(4): 641-644 (1983)
36. A. C. C. Yao. Separating the Polynomial-Time Hierarchy by Oracles FOCS 1985: 1-10