Certain decompositions of Gödel numbering and the semantics of programming languages

  • B. Buchberger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5)


Programming Language Cellular Automaton Recursive Function Large Oscillation Springer Lecture Note 
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  1. ASSER 60.
    G.Asser, Rekursive Wortfunktionen, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 6, pp.258–278.Google Scholar
  2. BEKIC/WALK 71.
    H.Bekic, K.Walk, Formalization of storage properties, in: Symposium on Semantics of Algorithmic Languages (E.Engeler ed.), Springer Lecture Notes 188, 1971.Google Scholar
  3. BLUM 67.
    M.Blum, A machine-independent theory of the complexity of recursive functions, J.ACM 14/2, 1967.Google Scholar
    B.Buchberger, Associating functions and the operator of conditioned iteration (Russian), Communications of the JINR Dubna, P5-5788, (English translation: Bericht Nr.71–1, Inst.f.num. Math., Univ.Innsbruck, 1971).Google Scholar
    B.Buchberger, A basic problem in the theory of programming languages, Bericht Nr.72–1, Inst.f.num.Math., Univ.Innsbruck, 1972.Google Scholar
    B.Buchberger, B.Roider, A study on universal functions, Bericht Nr.72–5, Inst.f.num.Math., Univ.Innsbruck, to appear.Google Scholar
  7. CODD 68.
    E.F.Codd, Cellular automata, Academic Press, 1968.Google Scholar
  8. FENSTAD 72.
    J.E.Fenstad, On axioms for computation theories, Lecture given at the conference on mathematical logic, Oberwolfach, Germany, April 1972.Google Scholar
  9. GILMORE 67.
    P.C.Gilmore, An abstract computer with a LISP-like machine language, in: Computer Programming and Formal Systems (P.Braffort/D.Hirschberg ed.), North-Holland, 1967.Google Scholar
    P.Lucas, P.Lauer, H.Stigleitner, Method and notation for the formal definition of programming languages, TR 25.087, IBM Laboratory Vienna, 1968.Google Scholar
  11. McCARTHY 62.
    J.McCarthy, LISP 1.5 programmer's manual, MIT Press, 1962.Google Scholar
    J.McCarthy, J.Painter, Correctness of a compiler for arithmetic expressions, Proc.of Applied Math. 19 (J.T. Schwartz ed.), Amer.Math.Soc., pp.33–41.Google Scholar
  13. MARKOV 47.
    A.A.Markov, On the representation of recursive functions (Russian), Doklady Ak.Nauk SSSR, n.s.58, pp.1891–1892.Google Scholar
    Axioms for computation theories — first draft, in: Logic Colloquium '69 (R.O.Gandy, C.M.E.Yates ed.), North-Holland, 1971.Google Scholar
  15. ROGERS 58.
    H. Rogers, Jr., Gödel numberings of partial recursive functions, J.Symbolic Logic 23/3, pp.331–341, 1958.Google Scholar
  16. ROGERS 67.
    H.Rogers, Jr., Theory of recursive functions and effective computability, McGraw-Hill 1967.Google Scholar
  17. SCHWENKEL 66.
    F. Schwenkel, Semantische Theorie der Programmiersprachen, Dissertation, Univ.Tübingen, Germany, 1966.Google Scholar
  18. SCOTT 67.
    D. Scott, Some definitional suggestions for automata theory, J.Comp.System Sci. 1, pp.187–212, 1967.Google Scholar
  19. SCOTT 71.
    D.Scott, The lattice of flow diagrams, in: Symposium on Semantics of Algorithmic Languages (E.Engeler ed.), Springer Lecture Notes 188, 1971.Google Scholar
  20. SHOENFIELD 71.
    J.R.Shoenfield, Degrees of unsolvability, North-Holland/American Elsevier, 1971.Google Scholar
  21. USPENSKII 56.
    V.A.Uspenskii, Computable operators and the notion of program (Russian), Uspehi Mat.Nauk 11/4, pp.172–176.Google Scholar
  22. USPENSKII 60.
    V.A. Uspenskii, Lectures on computable functions (Russian), Gos.Izd.Fiz.Mat.Lit., Moscow, 1960.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • B. Buchberger
    • 1
  1. 1.Inst. f. Num. Mathematik und Elektronische InformationsverarbeitungUniversität InnsbruckInnsbruckAustria/Europe

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