Abstract
We develop techniques for proving that specific families are not p-definable. As an application, we clarify the relation between several complexity classes: VP is strictly contained in VQP, but VQP is not contained in VNP. These separations are proven by means of specific p-families. Finally, we establish a connection between Valiant’s model and the Blum-Shub-Smale model, and outline possible directions for deepening our understanding of this connection.
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© 2000 Springer-Verlag Berlin Heidelberg
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Bürgisser, P. (2000). Separation Results and Future Directions. In: Completeness and Reduction in Algebraic Complexity Theory. Algorithms and Computation in Mathematics, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04179-6_8
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DOI: https://doi.org/10.1007/978-3-662-04179-6_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08604-5
Online ISBN: 978-3-662-04179-6
eBook Packages: Springer Book Archive