论文信息 - Complete Problems for Valiant's Class of qp-Computable Families of Polynomials

Complete Problems for Valiant's Class of qp-Computable Families of Polynomials

We prove that the families matrix powering, iterated matrix product, and adjoint matrix are VQP-complete, where VQP denotes Valiant's class of quasipolynomial-computable families of multivariate polynomials. This proves a conjecture by Burgisser [3, Conjecture 8.1].

Markus Bläser | M. Bläser

[1] Michael Ben-Or,et al. Computing Algebraic Formulas Using a Constant Number of Registers , 1992, SIAM J. Comput..

[2] Gary L. Miller,et al. Efficient Parallel Evaluation of Straight-Line Code and Arithmetic Circuits , 1988, SIAM J. Comput..

[3] Leslie G. Valiant,et al. Fast Parallel Computation of Polynomials Using Few Processors , 1983, SIAM J. Comput..

[4] Stephen A. Cook,et al. A Taxonomy of Problems with Fast Parallel Algorithms , 1985, Inf. Control..

[5] Joachim von zur Gathen,et al. Feasible Arithmetic Computations: Valiant's Hypothesis , 1987, J. Symb. Comput..

[6] Michael Clausen,et al. Algebraic complexity theory , 1997, Grundlehren der mathematischen Wissenschaften.

[7] Leslie G. Valiant,et al. The Complexity of Computing the Permanent , 1979, Theor. Comput. Sci..

[8] Laurent Hyafil. On the Parallel Evaluation of Multivariate Polynomials , 1979, SIAM J. Comput..

[9] Peter Bürgisser,et al. Completeness and Reduction in Algebraic Complexity Theory , 2000, Algorithms and computation in mathematics.

[10] S. Smale,et al. On a theory of computation and complexity over the real numbers; np-completeness , 1989 .

[11] Leslie G. Valiant,et al. Completeness classes in algebra , 1979, STOC.

[12] Laurent Hyafil,et al. On the parallel evaluation of multivariate polynomials , 1978, SIAM J. Comput..