On the relation between polynomial identity testing and finding variable disjoint factors

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

Volumn 6198 LNCS, Issue PART 1, 2010, Pages 408-419

  Shpilka, Amir ^a   Volkovich, Ilya ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ARITHMETIC CIRCUIT; BLACK BOXES; DECOMPOSITION PROBLEMS; DERANDOMIZING; DISJOINT SETS; MULTILINEAR POLYNOMIALS; POLYNOMIAL FACTORIZATION; POLYNOMIAL IDENTITY TESTING; POLYNOMIAL-TIME;

ALGORITHMS; FACTORIZATION; LINEAR ALGEBRA; LINGUISTICS; POLYNOMIAL APPROXIMATION; TRANSLATION (LANGUAGES);

EQUIVALENCE CLASSES;

EID: 77955315480     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-14165-2_35     Document Type: Conference Paper

References (36)

1. Kabanets, V., Impagliazzo, R.: Derandomizing polynomial identity tests means proving circuit lower bounds. Computational Complexity 13 (1- 2), 1-46 (2004)
2. Shpilka, A., Volkovich, I.: Read-once polynomial identity testing. In: Proceedings of the 40th Annual STOC, pp. 507-516 (2008)
3. Gathen, J.v. z., Gerhard, J.: Modern computer algebra. Cambridge University Press, Cambridge (1999)
4. Kaltofen, E.: Polynomial factorization: a success story. In: ISSAC, pp. 3-4 (2003)
5. Gathen, J.v. z.: Who was who in polynomial factorization. In: ISSAC, vol. 2 (2006)
6. Kayal, N.: Derandomizing some number-theoretic and algebraic algorithms. PhD thesis, Indian Institute of Technology, Kanpur, India (2007)
7. Agrawal, M., Kayal, N., Saxena, N.: Primes is in P. Annals of Mathematics 160 (2), 781-793 (2004)
8. Mulmuley, K., Vazirani, U., Vazirani, V.: Matching is as easy as matrix inversion. Combinatorica 7 (1), 105-113 (1987)
9. Schwartz, J. T.: Fast probabilistic algorithms for verification of polynomial identities. JACM 27 (4), 701-717 (1980)
10. Zippel, R.: Probabilistic algorithms for sparse polynomials. In: Symbolic and algebraic computation, pp. 216-226 (1979)
11. DeMillo, R. A., Lipton, R. J.: A probabilistic remark on algebraic program testing. Inf. Process. Lett. 7 (4), 193-195 (1978)
12. Klivans, A., Spielman, D.: Randomness efficient identity testing of multivariate polynomials. In: Proceedings of the 33rd Annual STOC, pp. 216-223 (2001)
13. Agrawal, M., Biswas, S.: Primality and identity testing via chinese remaindering. JACM 50 (4), 429-443 (2003)
14. Lipton, R. J., Vishnoi, N. K.: Deterministic identity testing for multivariate polynomials. In: Proceedings of the 14th annual SODA, pp. 756-760 (2003)
15. 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)
16. Raz, R., Shpilka, A.: Deterministic polynomial identity testing in non commutative models. Computational Complexity 14 (1), 1-19 (2005)
17. Dvir, Z., Shpilka, A.: Locally decodable codes with 2 queries and polynomial identity testing for depth 3 circuits. SIAM J. on Computing 36 (5), 1404-1434 (2006)
18. Kayal, N., Saxena, N.: Polynomial identity testing for depth 3 circuits. Computational Complexity 16 (2), 115-138 (2007)
19. Arvind, V., Mukhopadhyay, P.: The monomial ideal membership problem and polynomial identity testing. In: Proceedings of the 18th ISAAC, pp. 800-811 (2007)
20. 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 Annual CCC, pp. 280-291 (2008)
21. Saxena, N., Seshadhri, C.: An almost optimal rank bound for depth-3 identities. In: Proceedings of the 24th annual CCC (2009)
22. Dvir, Z., Shpilka, A., Yehudayoff, A.: Hardness-randomness tradeoffs for bounded depth arithmetic circuits. SIAM J. on Computing 39 (4), 1279-1293 (2009)
23. Agrawal, M., Vinay, V.: Arithmetic circuits: A chasm at depth four. In: Proceedings of the 49th Annual FOCS, pp. 67-75 (2008)
24. Arvind, V., Mukhopadhyay, P.: Derandomizing the isolation lemma and lower bounds for circuit size. In: Goel, A., Jansen, K., Rolim, J. D. P., Rubinfeld, R. (eds.) APPROX and RANDOM 2008. LNCS, vol. 5171, pp. 276-289. Springer, Heidelberg (2008)
25. Kayal, N., Saraf, S.: Blackbox polynomial identity testing for depth 3 circuits. Electronic Colloquium on Computational Complexity (ECCC), (32) (2009)
26. Shpilka, A., Volkovich, I.: Improved polynomial identity testing for read-once formulas. In: APPROX-RANDOM, pp. 700-713 (2009)
27. Karnin, Z. S., Mukhopadhyay, P., Shpilka, A., Volkovich, I.: Deterministic identity testing of depth 4 multilinear circuits with bounded top fan-in. In: Proceedings of the 42th Annual STOC (2010)
28. Saxena, N., Seshadhri, C.: From sylvester-gallai configurations to rank bounds: Improved black-box identity test for depth-3 circuits. Electronic Colloquium on Computational Complexity (ECCC) (013) (2010)
29. Heintz, J., Schnorr, C. P.: Testing polynomials which are easy to compute (extended abstract). In: Proceedings of the 12th annual STOC, pp. 262-272 (1980)
30. Raz, R.: Multi-linear formulas for permanent and determinant are of superpolynomial size. In: Proceedings of the 36th Annual STOC, pp. 633-641 (2004)
31. 2. In: Proceedings of the 45th Annual FOCS, pp. 344-351 (2004)
32. Raz, R., Shpilka, A., Yehudayoff, A.: A lower bound for the size of syntactically multilinear arithmetic circuits. SIAM J. on Computing 38 (4), 1624-1647 (2008)
33. Raz, R., Yehudayoff, A.: Lower bounds and separations for constant depth multilinear circuits. In: IEEE Conference on Computational Complexity, pp. 128-139 (2008)
34. Hancock, T. R., Hellerstein, L.: Learning read-once formulas over fields and extended bases. In: Proceedings of the 4th Annual COLT, pp. 326-336 (1991)
35. Bshouty, N. H., Hancock, T. R., Hellerstein, L.: Learning arithmetic read-once formulas. SIAM J. on Computing 24 (4), 706-735 (1995)
36. Kaltofen, E., Koiran, P.: On the complexity of factoring bivariate supersparse (lacunary) polynomials. In: ISSAC, pp. 208-215 (2005)