Improved polynomial identity testing for read-once formulas

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5687 LNCS, Issue , 2009, Pages 700-713

  Shpilka, Amir ^a   Volkovich, Ilya ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

BLACK BOXES; DETERMINISTIC ALGORITHMS; GENERAL MODEL; HITTING SETS; IDENTITY TESTING; INPUT VARIABLES; NEW RESULTS; POLYNOMIAL IDENTITY TESTING; READ-ONCE FORMULAS; RECONSTRUCTION ALGORITHMS; UNDERLYING GRAPHS;

COMBINATORIAL OPTIMIZATION; HARDNESS; HARDNESS TESTING; POLYNOMIALS; TECHNICAL PRESENTATIONS;

APPROXIMATION ALGORITHMS;

EID: 70350583384     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-03685-9_52     Document Type: Conference Paper

References (28)

1. Agrawal, M.: Proving lower bounds via pseudo-random generators. In: Sarukkai, S., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 92-105. Springer, Heidelberg (2005)
2. Agrawal, M., Biswas, S.: Primality and identity testing via chinese remaindering. JACM 50(4), 429-443 (2003)
3. Agrawal, M., Vinay, V.: Arithmetic circuits: A chasm at depth four. In: Proceedings of the 49th FOCS, pp. 67-75 (2008)
4. Arvind, V., Mukhopadhyay, P.: The monomial ideal membership problem and polynomial identity testing. In: Tokuyama, T. (ed.) ISAAC 2007. LNCS, vol. 4835, pp. 800-811. Springer, Heidelberg (2007)
5. Ben-Or, M., Tiwari, P.: A deterministic algorithm for sparse multivariate polynomial interpolation. In: Proceedings of the 20th STOC, pp. 301-309 (1988)
6. Bshouty, D., Bshouty, N.H.: On interpolating arithmetic read-once formulas with exponentiation. J. of Computer and System Sciences 56(1), 112-124 (1998)
7. Bshouty, N.H., Hancock, T.R., Hellerstein, L.: Learning arithmetic read-once formulas. SICOMP 24(4), 706-735 (1995)
8. Chen, Z., Kao, M.: Reducing randomness via irrational numbers. In: Proceedings of the 29th STOC, pp. 200-209 (1997)
9. Dvir, Z., Shpilka, A.: Locally decodable codes with 2 queries and polynomial identity testing for depth 3 circuits. SICOMP 36(5), 1404-1434 (2006)
10. Dvir, Z., Shpilka, A., Yehudayoff, A.: Hardness-randomness tradeoffs for bounded depth arithmetic circuits. In: Proceedings of the 40th STOC, pp. 741-748 (2008)
11. Hancock, T.R., Hellerstein, L.: Learning read-once formulas over fields and extended bases. In: Proceedings of the 4th COLT, pp. 326-336 (1991)
12. Kabanets, V., Impagliazzo, R.: Derandomizing polynomial identity tests means proving circuit lower bounds. Computational Complexity 13(1-2), 1-46 (2004)
13. Karnin, Z.S., Shpilka, A.: Deterministic black box polynomial identity testing of depth-3 arithmetic circuits with bounded top fan-in. In: Proceedings of the 23rd CCC, pp. 280-291 (2008)
14. Kayal, N., Saxena, N.: Polynomial identity testing for depth 3 circuits. Computational Complexity 16(2), 115-138 (2007)
15. Klivans, A., Spielman, D.: Randomness efficient identity testing of multivariate polynomials. In: Proceedings of the 33rd STOC, pp. 216-223 (2001)
16. Lewin, D., Vadhan, S.: Checking polynomial identities over any field: Towards a derandomization? In: Proceedings of the 30th STOC, pp. 428-437 (1998)
17. Lipton, R.J., Vishnoi, N.K.: Deterministic identity testing for multivariate polynomials. In: Proceedings of the 14th SODA, pp. 756-760 (2003)
18. 2. In: Proceedings of the 45th FOCS, pp. 344-351 (2004)
19. Raz, R.: Extractors with weak random seeds. In: Proceedings of the 37th STOC, pp. 11-20 (2005)
20. Raz, R., Shpilka, A.: Deterministic polynomial identity testing in non commutative models. Computational Complexity 14(1), 1-19 (2005)
21. Raz, R., Shpilka, A., Yehudayoff, A.: A lower bound for the size of syntactically multilinear arithmetic circuits. SICOMP 38(4), 1624-1647 (2008)
22. Raz, R., Yehudayoff, A.: Lower bounds and separations for constant depth multilinear circuits. In: 40th CCC, pp. 128-139 (2008)
23. Saxena, N.: Diagonal circuit identity testing and lower bounds. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 60-71. Springer, Heidelberg (2008)
24. Saxena, N., Seshadhri, C.: An almost optimal rank bound for depth-3 identities. CoRR, abs/0811.3161 (2008)
25. Schwartz, J.T.: Fast probabilistic algorithms for verification of polynomial identities. JACM 27(4), 701-717 (1980)
26. Shpilka, A.: Interpolation of depth-3 arithmetic circuits with two multiplication gates. SICOMP 38(6), 2130-2161 (2009)
27. Shpilka, A., Volkovich, I.: Read-once polynomial identity testing. In: Proceedings of the 40th STOC, pp. 507-516 (2008)
28. Zippel, R.: Probabilistic algorithms for sparse polynomials. In: Symbolic and algebraic computation, pp. 216-226 (1979)