The Complexity of Semilinear Problems in Succinct Representation

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 PNP[log]-completeness of deciding Zariski irreducibility, exhibits for the first time a problem with a geometric nature complete in this class. Keywords. BSS additive model, semilinear sets, complete problems. Subject classification. 68Q15.

• Type: Conference
• Year: 2005
• Where: FCT
• Authors: Peter Bürgisser, Felipe Cucker, Paulin Jacobé de Naurois
• Keywords: Additive Model, Blum-Shub-Smale Additive Model, FCT 2005, Semilinear Sets