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On r.e. inseparability of CPO index sets

  • Dieter Spreen
Section I: Complexity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 171)

Abstract

In this paper the r.e. inseparability and the effective r.e. inseparability of index sets under certain indexings of the computable elements of an effective cpo are studied. As a consequence of the main result on effective r.e. inseparability we obtain a generalization of a theorem by McNaughton. As a further application we obtain generalizations of results by Myhill/Dekker on the productivity of certain index sets. From this we infer the generalization of theorems by Rice/Shapiro/McNaughton/Myhill and Myhill/Shepherdson. This demonstrates the importance of the r.e. inseparability notion.

Keywords

Recursive Function Relative Topology Computable Element Directed Subset Partial Recursive Function 
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References

  1. [1]
    Case, J.: private communication (1982).Google Scholar
  2. [2]
    Egli, H.; Constable, R.L.: Computability concepts for programming language semantics. Theoret. Comp. Sci. 2, 133–145 (1976).Google Scholar
  3. [3]
    Eršov, Ju. L.: Theorie der Numerierungen I. Zeitschr. f. Math. Logik u. Grundl. d. Math. 19, 289–388 (1973).Google Scholar
  4. [4]
    Gierz, G. et. al.: A Compendium of Continuous Lattices. Berlin: Springer (1980).Google Scholar
  5. [5]
    Kanda, A.; Park, D.: When are two effectively given domains identical? 4th GI Conference Theoretical Comput. Sci., Aachen 1979, Lec. Notes Comput. Sci. 67, 170–181 (1979).Google Scholar
  6. [6]
    Myhill, J.; Dekker, J.C.E.: Some theorems on classes of recursively enumerable sets. Transact. AMS 89, 29–59 (1958).Google Scholar
  7. [7]
    Plotkin, G.: Пω as a universal domain. J. Computer Syst. Sci. 17, 209–236 (1978).Google Scholar
  8. [8]
    Rogers, H., Jr.: Theory of Recursive Functions and Effective Computability. New York: McGraw-Hill (1967).Google Scholar
  9. [9]
    Scott, D.: Outline of a mathematical theory of computation. Techn. Monograph PRG-2, Oxford Uni. Comp. Lab. (1970).Google Scholar
  10. [10]
    Sciore, E.; Tang, A.: Admissible coherent cpo-s. Automata, Languages and Programming, 5th Colloq., Udine 1978, Lec. Notes Comput. Sci. 62, 440–456 (1978).Google Scholar
  11. [11]
    Smyth, M.B.: Effectively given domains. Theoret. Comp. Sci. 257–274 (1973).Google Scholar
  12. [12]
    Weihrauch, K.; Deil, Th.: Berechenbarkeit auf cpo-s. Schriften zur Angew. Math. u. Informatik Nr. 63, RWTH Aachen (1980).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Dieter Spreen
    • 1
  1. 1.Lehrstuhl für Informatik IRheinisch-Westfälische Technische Hochschule AachenAachenWest Germany

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