On Algebraic Branching Programs of Small Width

@article{Bringmann2018OnAB,
  title={On Algebraic Branching Programs of Small Width},
  author={K. Bringmann and Christian Ikenmeyer and Jeroen Zuiddam},
  journal={ArXiv},
  year={2018},
  volume={abs/1702.05328}
}
In 1979, Valiant showed that the complexity class VPe of families with polynomially bounded formula size is contained in the class VPs of families that have algebraic branching programs (ABPs) of polynomially bounded size. Motivated by the problem of separating these classes, we study the topological closure VPe, i.e., the class of polynomials that can be approximated arbitrarily closely by polynomials in VPe. We describe VPe using the well-known continuant polynomial (in characteristic… Expand
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References

SHOWING 1-6 OF 6 REFERENCES
Computing Algebraic Formulas Using a Constant Number of Registers
  • 151
  • Highly Influential
Completeness classes in algebra
  • 513
  • Highly Influential
On the power of algebraic branching programs of width two
  • 16
  • Highly Influential
  • PDF
Arithmetic Circuits: A Chasm at Depth Four
  • Manindra Agrawal, V. Vinay
  • Mathematics, Computer Science
  • 2008 49th Annual IEEE Symposium on Foundations of Computer Science
  • 2008
  • 205
  • Highly Influential
  • PDF
The Parallel Evaluation of General Arithmetic Expressions
  • R. Brent
  • Mathematics, Computer Science
  • JACM
  • 1974
  • 840
  • Highly Influential
  • PDF
Reducibility by Algebraic Projections
  • 1980