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Index Sets as a Measure of Continuous Constraint Complexity

  • Margarita Korovina
  • Oleg Kudinov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8974)

Abstract

We develop the theory of index sets in the context of computable analysis considering classes of effectively open sets and computable real-valued functions. First, we construct principal computable numberings for effectively open sets and computable real-valued functions. Then, we calculate the complexity of index sets for important problems such as root realisability, set equivalence and inclusion, function equivalence which naturally arise in continuous constraint solving. Using developed techniques we give a direct proof of the generalised Rice-Shapiro theorem for effectively open sets of Euclidean spaces and present an analogue of Rice’s theorem for computable real-valued functions. We illustrate how index sets can be used to estimate complexity of continuous constraints in the settings of the Kleene-Mostowski arithmetical hierarchy.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.A.P. Ershov Institute of Informatics SystemsNovosibirskRussia
  2. 2.Sobolev Institute of MathematicsNovosibirskRussia

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