Exponential lower bounds for depth 3 arithmetic circuits in algebras of functions over finite fields

Applicable Algebra in Engineering, Communications and Computing

Volumn 10, Issue 6, 2000, Pages 465-487

  Grigoriev, D ^a   Razborov, A ^b  

^a UNIVERSITÉ DE RENNES 1   (France)

^b STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

BOOLEAN FUNCTIONS; BOUNDARY CONDITIONS; COMPUTATIONAL COMPLEXITY; DIGITAL ARITHMETIC; MATRIX ALGEBRA; SET THEORY; THEOREM PROVING;

ARITHMETIC CIRCUITS; EXPONENTIAL LOWER BOUNDS; FINITE FIELDS; LINEAR FUNCTIONS; MULTIPLICATIVE COMPLEXITY;

MULTIPLYING CIRCUITS;

EID: 0033699197     PISSN: 09381279     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002009900021     Document Type: Article

References (22)

1. 0, and arithmetic circuits. ECCC Report TR97-016
2. Baur, W., Strassen, V.: The complexity of partial derivatives. Theor. Comput. Sci. 22, 317-330 (1983)
3. Chernoff, H.: A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Annals of Math. Stat. 23, 493-509 (1952)
4. Friedman, J.: A note on matrix rigidity. Combinatorica 13, 235-239 (1993)
5. von zur Gathen, J.: Feasible arithmetic computations: Valiant's hypothesis. J. Symp. Comput. 4, 137-172 (1987)
6. Russian source
7. (English transl.: D. Grigoriev. Using the notions of separability and independence for proving lower bounds on the circuit complexity. J. Soviet Math. vol. 14, 5, pp. 1450-1456 (1980)
8. Russian source
9. English transl.: D. Grigoriev. Lower bounds in algebraic complexity. J. Soviet Math. 29, pp. 1388-1425 (1985)
10. Grigoriev, D.: Testing shift-equivalence of polynomials by deterministic, probabilistic and quantum machines. Theor. Comput. Sci. 180, 217-228 (1997)
11. Grigoriev, D., Karpinski, M.: An exponential lower bound for depth 3 arithmetic circuits. Proc. ACM Symp. Th. Comput. Dallas, pp. 577-582 (1998)
12. Grigoriev, D., Razborov, A.: Exponential complexity lower bounds for depth 3 arithmetic circuits in algebras of functions over finite fields. Proc. IEEE Symp. Found. Comput. Sci. Palo Alto, pp. 269-278 (1998)
13. Nisan, N., Wigderson, A.: Lower bound on arithmetic circuits via partial derivatives. Proc. IEEE Symp. Found. Comput. Sci. pp. 16-25 (1995)
14. Russian source
15. Engl. transl.: A. Razborov. Lower bounds on the size of bounded depth circuits over a complete basis with logical addition. Math. Notes 41, 333-338 (1987)
16. Shpilka, A., Wigderson, A.: Depth-3 arithmetic formulae over fields of characteristic zero, Manuscript 1998
17. Smolensky, R.: Algebraic methods in the theory of lower bounds for boolean circuit complexity. Proc. ACM Symp. Th. Comput. pp. 77-82 (1987)
18. Strassen, V.: Die Berechnungskomplexität von Elementarsymmetrischen Funktionen und von Interpolationskoeffizienten. Numer. Math. 20, 238-251 (1973)
19. Valiant, L.: Graph-theoretic arguments in low-level complexity. Proceedings of the 6th MFCS, Lecture Notes in Computer Science 53, pp. 162-176 (1977)
20. Valiant, L.: Completeness classes in algebra. Proc. ACM Symp. Th. Comput 259-261 (1979)
21. van der Geer, G., van Lint, J.: Introduction to Coding Theory and Algebraic Geometry. Basel Birkhaüser 1988
22. van Lint, J.: Introduction to Coding Theory. Berlin Heidelberg New York: Springer 1982