The Complexity of Semilinear Problems in Succinct Representation

  • Peter Bürgisser
  • Felipe Cucker
  • Paulin Jacobé de Naurois
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3623)


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.


Polynomial Time Irreducible Component Feasibility Problem Zariski Closure Input Gate 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Peter Bürgisser
    • 1
  • Felipe Cucker
    • 2
  • Paulin Jacobé de Naurois
    • 3
  1. 1.Dept. of MathematicsUniversity of PaderbornPaderbornGermany
  2. 2.Department of MathematicsCity University of Hong KongHong KongP.R. of China
  3. 3.LORIAVillers-lès-Nancy Cedex, NancyFrance

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