Succinct representations of graphs
Information and Control
Feasible arithmetic computations: Valiant's hypothesis
Journal of Symbolic Computation
Computing algebraic formulas using a constant number of registers
SIAM Journal on Computing
Circuit definitions of nondeterministic complexity classes
SIAM Journal on Computing
Succinct representation, leaf languages, and projection reductions
Information and Computation
Completeness classes in algebra
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
The Complexity of Polynomials and Their Coefficient Functions
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Characterizing Valiant's algebraic complexity classes
Journal of Complexity
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
VPSPACE and a Transfer Theorem over the Reals
Computational Complexity
Functions computable in polynomial space
Information and Computation
Small-space analogues of Valiant's classes
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Counting classes and the fine structure between NC1and L
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
On the complexity of the multivariate resultant
Journal of Complexity
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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 theHamiltonian 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.