Interpolating arithmetic read-once formulas in parallel

SIAM Journal on Computing

Volumn 27, Issue 2, 1998, Pages 401-413

  Bshouty, Nader H ^a   Cleve, Richard ^a  

^a UNIVERSITY OF CALGARY   (Canada)

Author keywords

Learning theory; Parallel algorithm; Read once formula

Indexed keywords

EID: 1542569418     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S009753979528812X     Document Type: Article

References (26)

1. [A87] D. ANGLUIN, Queries and concept learning, Mach. Learning, 2 (1987), p. 319-342.
2. [AHK89] D. ANGLUIN, L. HELLERSTEIN, AND M. KARPINSKI, Learning read-once formulas with queries, J. ACM, 40 (1993), pp. 185-210.
3. [AK91] D. ANGLUIN AND M. KHARITONOV, When won't membership queries help?, J. Comput. System Sci., 50 (1995), pp. 336-355.
4. [B74] J. P. BRENT, The parallel evaluation of general arithmetic expressions, J. ACM, 21 (1974), pp. 201-206.
5. [BHH92] N. H. BSHOUTY, T. R. HANCOCK, AND L. HELLERSTEIN, Learning arithmetic readonce formulas, SIAM J. Comput., 24 (1995), pp. 706-735.
6. [BC92] N. H. BSHOUTY AND R. CLEVE, On the exact learning of formulas in parallel, Proc. of the 33rd Annual Symposium on Foundations of Computer Science, IEEE Computer Science Press, Los Alamitos, CA, 1992, pp. 24-27.
7. [B2H92] N. H. BSHOUTY, T. R. HANCOCK, AND L. HELLERSTEIN, Learning boolean read-once formulas with arbitrary symmetric and constant fan-in gates, J. Comput. System Sci., 50 (1995), pp. 521-542.
8. [BGHM93] N. H. BSHOUTY, S. GOLDMAN, T. HANCOCK, AND S. MATAR, Asking questions to minimize errors, in Proc. of the Sixth Annual Workshop on Computational Learning Theory, ACM, New York, 1993, pp. 41-50.
9. [BHHK91] N. H. BSHOUTY, T. R. HANCOCK, L. HELLERSTEIN, AND M. KARPINSKI, An algorithm to learn read-once threshold formulas, and transformation between learning models, Comput. Complexity, 4 (1994), pp. 37-61.
10. [BT88] M. BEN-OR AND P. TIWARI, A deterministic algorithm for sparse multivariate polynomial interpolation, in Proc. of the 20th Annual ACM Symposium on the Theory of Computing, ACM, New York, 1988, pp. 301-309.
11. [BT90] A. BORODIN AND P. TIWARI, On the decidability of sparse univariate polynomial interpolation, Comput. Complexity, 1 (1991), pp. 67-90.
12. [GKS90a] S. A. GOLDMAN, M. J. KEARNS, AND R. E. SCHAPIRE, Exact identification of read-once formulas using fixed points of amplification functions, SIAM J. Comput., 22 (1993), pp. 705-726.
13. [GKS88] D. Y. GRIGORIEV, M. KARPINSKI, AND M. F. SINGER, Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields, SIAM J. Comput., 19 (1990), pp. 1059-1083.
14. [GKS90b] D. Y. GRIGORIEV, M. KARPINSKI, AND M. F. SINGER, Interpolation of sparse rational functions without knowing bounds on the exponent, in Proc. of the 31st Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1990, pp. 193-202.
15. [Han90] T. HANCOCK, Identifying μ-formula decision trees with queries, in Proc. of the Third Annual Workshop on Computational Learning Theory, ACM, New York, 1990, pp. 23-37.
16. [HH91] T. HANCOCK AND L. HELLERSTEIN, Learning read-once formulas over fields and extended bases, in Proc. of the Fourth Annual Workshop on Computational Learning Theory, ACM, New York, 1991, pp. 326-336.
17. [HS80] J. HEINTZ AND C. P. SCHNORR, Testing polynomials that are easy to compute, in Proc. of the 12th Annual ACM Symposium on the Theory of Computing, ACM, New York, 1980, pp. 262-272.
18. [LF80] R. E. LADNER AND M. J. FISCHER, Parallel prefix computation, J. ACM, 27 (1980), pp. 831-838.
19. [L88] N. LITTLESTONE, Learning quickly when irrelevant attributes abound: A new linear threshold algorithm, Mach. Learning, 2 (1988), pp. 285-318.
20. [M91] Y. MANSOUR, Randomized approximation and interpolation of sparse polynomials, SIAM J. Comput., 24 (1995), pp. 357-368.
21. [MT90] W. MAASS AND G. TURÁN, On the complexity of learning from counterexamples and membership queries, in Proc. of the 31st Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1990, pp. 203-210.
22. [RB89] M. R. ROTH AND G. M. BENEDEK, Interpolation and approximation of sparse multivariate polynomials over GF(2), SIAM J. Comput., 20 (1991), pp. 291-314.
23. [SS93] R. E. SCHAPIRE AND L. M. SELLIE, Learning sparse multivariate polynomials over a field with queries and counterexamples, J. Comput. Systems Sci., 52 (1996), pp. 201-213.
24. [Sch80] J. T. SCHWARTZ, Fast polynomial algorithms for verification of polynomial identities, J. Assoc. Comput. Mach., 27 (1980), pp. 701-707.
25. [Val84] L. G. VALIANT, A theory of the learnable, Comm. ACM, 27 (1984), pp. 1134-1142.
26. [VL92] J. S. VITTER AND J. LIN, Learning in parallel, Inform, and Comput., 96 (1992), pp. 179-202.