On the exact learning of formulas in parallel

The authors investigate the parallel complexity of learning formulas from membership and equivalence queries. They consider a number of learning problems that can be solved sequentially in polynomial time. They prove some upper and lower bounds on the number of parallel steps required to solve these problems with a polynomial number of processors.<<ETX>>

[1]  Dana Angluin,et al.  When won't membership queries help? , 1991, STOC '91.

[2]  Ron M. Roth,et al.  Interpolation and Approximation of Sparse Multivariate Polynomials over GF(2) , 1991, SIAM J. Comput..

[3]  Marek Karpinski,et al.  Learning read-once formulas with queries , 1993, JACM.

[4]  Wolfgang Maass,et al.  On the complexity of learning from counterexamples and membership queries , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[5]  Lisa Hellerstein,et al.  Learning Boolean read-once formulas with arbitrary symmetric and constant fan-in gates , 1992, COLT '92.

[6]  Lisa Hellerstein,et al.  Learning read-once formulas over fields and extended bases , 1991, COLT '91.

[7]  Lisa Hellerstein,et al.  Learning arithmetic read-once formulas , 1992, STOC '92.

[8]  Jacob T. Schwartz,et al.  Fast Probabilistic Algorithms for Verification of Polynomial Identities , 1980, J. ACM.

[9]  Richard P. Brent,et al.  The Parallel Evaluation of General Arithmetic Expressions , 1974, JACM.

[10]  Thomas R. Hancock,et al.  Identifying μ-formula decision trees with queries , 1990, COLT '90.

[11]  Marek Karpinski,et al.  Fast Parallel Algorithms for Sparse Multivariate Polynomial Interpolation over Finite Fields , 1988, SIAM J. Comput..

[12]  Michael Ben-Or,et al.  A deterministic algorithm for sparse multivariate polynomial interpolation , 1988, STOC '88.

[13]  Jeffrey Scott Vitter,et al.  Learning in parallel , 1988, COLT '88.

[14]  Marek Karpinski,et al.  Interpolation of sparse rational functions without knowing bounds on exponents , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[15]  Leslie G. Valiant,et al.  A theory of the learnable , 1984, STOC '84.

[16]  Allan Borodin,et al.  On the decidability of sparse univariate polynomial interpolation , 1990, STOC '90.