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The Complexity of Semilinear Problems in Succinct Representation

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 3623)

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.

Keywords

  • Polynomial Time
  • Irreducible Component
  • Feasibility Problem
  • Zariski Closure
  • Input Gate

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bürgisser, P., Cucker, F., de Naurois, P.J. (2005). The Complexity of Semilinear Problems in Succinct Representation. In: Liśkiewicz, M., Reischuk, R. (eds) Fundamentals of Computation Theory. FCT 2005. Lecture Notes in Computer Science, vol 3623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537311_42

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  • DOI: https://doi.org/10.1007/11537311_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28193-1

  • Online ISBN: 978-3-540-31873-6

  • eBook Packages: Computer ScienceComputer Science (R0)