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Positive predicate structures for continuous data

  • MARGARITA KOROVINA (a1) and OLEG KUDINOV (a2)
Abstract

In this paper, we develop a general framework for continuous data representations using positive predicate structures. We first show that basic principles of Σ-definability which are used to investigate computability, i.e., existence of a universal Σ-predicate and an algorithmic characterization of Σ-definability hold on all predicate structures without equality. Then we introduce positive predicate structures and show connections between these structures and effectively enumerable topological spaces. These links allow us to study computability over continuous data using logical and topological tools.

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This research was partially supported by EU project PIRSES-GA-2011-294962, grants DFG/RFBR 1267/14-1, 14-01-91334 and RFBR 13-01-0015_a.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

M. Ajtai (1989) First-order definability on finite structures. Annals of Pure and Applied Logic 45 211225.

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M. Korovina (2003) Gandy's theorem for abstract structures without the equality test. In: Y. M. Vardi and A. Voronkov (eds.) LPAR'03, Springer Lecture Notes in Computer Science 2850 290301.

M. Korovina (2003) Computational aspects of Σ-definability over the real numbers without the equality test. In: M. Baaz and J. A. Makowsky (eds.) CSL'03, Springer Lecture Notes in Computer Science 2803 330344.

M. Korovina and O. Kudinov (2005) Towards computability of higher type continuous data. In: S. B Cooper ., B. Löwe and L. Torenvliet (eds) CiE'05, Springer Lecture Notes in Computer Science 3526 235241.

M. Korovina and O. Kudinov (2007) The uniformity principle for Σ-definability with applications to computable analysis. In: S. B. Cooper , B. Löwe and A. Sorbi (eds.) CiE'07, Springer Lecture Notes in Computer Science 4497 416425.

M. Korovina and O. Kudinov (2008) Towards Computability over Effectively Enumerable Topological Spaces. Elsevier Electronic Notes in Theoretical Computer Science 221 115125.

A. Morozov and M. Korovina (2008) On Σ-definability without equality over the real numbers. Mathematical Logic Quarterly 54 (5) 535544.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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