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The complexity of semilinear problems in succinct representation
Citation key BCN-The-Complexity-Of-Semilinear-Problems-In-Succinct-Representation
Author Peter Bürgisser and Felipe Cucker and Paulin Jacobé de Naurois
Pages 197-235
Year 2006
Journal Computational Complexity
Volume 15
Number 3
Abstract We prove completeness results for twenty three problems in semilinear geometry. These results involve semilinear sets given by additive circuits as input data. If arbitrary real constants are allowed in the circuit, the completeness results are for the Blum-Shub-Smale additive model of computation. If, in contrast, the circuit is constant-free, then the completeness results are for the Turing model of computation. One such result, the P^NP[log]-completeness of deciding Zariski irreducibility, exhibits for the first time a problem with a geometric nature complete in this class.
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