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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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Ajtai M. (1989) First-order definability on finite structures. Annals of Pure and Applied Logic 45 211225.
Barwise J. (1975) Admissible Sets and Structures. Springer Verlag.
Brattka V. and Presser G. (2003) Computability on subsets of metric spaces. Theoretical Computer Science 305 (1–3) 4376.
Ershov Y. L. (1996) Definability and Computability. Plenum, New York.
Grübba T., Schröder M. and Weihrauch K. (2007) Computable metrization. Mathematical Logic Quaterly 53 (4–5) 595604.
Hodges W. (1993) The meaning of specifications: Set-theoretical specification. Semantics of Programming Languages and Model Theory, Algebra, Logic and Applications Series 5 4368.
Immerman N. (1999) Descriptive Complexity. Springer Verlag.
Korovina M. (2003) Gandy's theorem for abstract structures without the equality test. In: Vardi Y. M. and Voronkov A. (eds.) LPAR'03, Springer Lecture Notes in Computer Science 2850 290301.
Korovina M. (2003) Computational aspects of Σ-definability over the real numbers without the equality test. In: Baaz M. and Makowsky J. A. (eds.) CSL'03, Springer Lecture Notes in Computer Science 2803 330344.
Korovina M. and Kudinov O. (2005) Towards computability of higher type continuous data. In: Cooper S. B., Löwe B. and Torenvliet L. (eds) CiE'05, Springer Lecture Notes in Computer Science 3526 235241.
Korovina M. and Kudinov O. (2007) The uniformity principle for Σ-definability with applications to computable analysis. In: Cooper S. B., Löwe B. and Sorbi A. (eds.) CiE'07, Springer Lecture Notes in Computer Science 4497 416425.
Korovina M. and Kudinov O. (2008) Towards Computability over Effectively Enumerable Topological Spaces. Elsevier Electronic Notes in Theoretical Computer Science 221 115125.
Morozov A. and Korovina M. (2008) On Σ-definability without equality over the real numbers. Mathematical Logic Quarterly 54 (5) 535544.
Moschovakis Y. N. (1969) Abstract first order computability I, II. Transactions of the American Mathematical Society 138 427504.
Moschovakis Y. N. (1974) Elementary induction on abstract structures. Studies in Logic and the Foundations of Mathematics volume 77, North-Holland.
Moschovakis Y. N. (1976) Recursive metric spaces. Fundamenta Mathematicae 55 215238.
Sazonov V. (2001) Using agents for concurrent querying of web-like databases via hyper-set-theoretic approach. In: Bjørner D., Broy M. and Zamulin A. V. (eds.) PSI'01, Springer Lecture Notes in Computer Science 2244 378394.
Weihrauch K. (1993) Computability on computable metric spaces. Theoretical Computer Science 113 191210.
Weihrauch K. (2000) Computable Analysis. Springer Verlag.
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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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