We study characterizations of algebraic complexity classes by branching programs of possibly exponential size, using a succinctness condition to replace the usual one based on uniformity. We obtain characterizations of VPSPACE, the class corresponding to computations in polynomial space, and observe that algebraic polynomial space can be seen as constant algebraic space with auxiliary polynomial space Boolean computations. We also obtain the first examples of natural complete polynomials for VPSPACE, in particular showing that polynomials like the determinant, the permanent or the Hamiltonian become VPSPACE-complete when the matrix is succinctly encoded. Using the same techniques we also characterize VNP. In general, we argue that characterizations by branching programs apply to different classes, both Boolean and algebraic, with or without uniformity, and thus provide a general and uniform technique in these different settings. © 2011 Springer-Verlag.
CITATION STYLE
Malod, G. (2011). Succinct algebraic branching programs characterizing non-uniform complexity classes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6914 LNCS, pp. 205–216). Springer Verlag. https://doi.org/10.1007/978-3-642-22953-4_18
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