Abstract
We treat Valiant’s algebraic theory of NP-compieteness in detail and give a simplified VNP-completeness proof for the family of permanents. Then we discuss various closure properties of the complexity classes VP and VNP, in particular closedness with respect to factors. We also prove the important result on the efficient parallelization of straight-line programs due to Valiant, Skyum, Berkowitz, and Rackoff. As an application, we deduce the completeness of the determinant family in the class of gp-computable families.
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© 2000 Springer-Verlag Berlin Heidelberg
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Bürgisser, P. (2000). Valiant’s Algebraic Model of NP-Completeness. 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_2
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DOI: https://doi.org/10.1007/978-3-662-04179-6_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08604-5
Online ISBN: 978-3-662-04179-6
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