Some Independence Results for Control Structures in Complete Numberings

Acceptable programming systems have many nice properties like s-m-n-Theorem, Composition and Kleene Recursion Theorem. Those properties are sometimes called control structures, to emphasize that they yield tools to implement programs in programming systems. It has been studied. among others by Riccardi and Royer. how these control structures influence or even characterize the notion of acceptable programming system. The following is an investigation, how these control structures behave in the more general setting of complete numberings as defined by Mal'cev and Ergov. ?

[1]  Donald H. Taranto.  Algorithms and recursive functions , 1968 .

[2]  D. C. Cooper,et al.  Theory of Recursive Functions and Effective Computability , 1969, The Mathematical Gazette.

[3]  Rusins Freivalds,et al.  How Inductive Inference Strategies Discover Their Errors , 1995, Inf. Comput..

[4]  Günter Asser,et al.  Zeitschrift für mathematische Logik und Grundlagen der Mathematik , 1955 .

[5]  Dana Angluin,et al.  Inductive Inference of Formal Languages from Positive Data , 1980, Inf. Control..

[6]  Thomas Zeugmann,et al.  Language learning in dependence on the space of hypotheses , 1993, COLT '93.

[7]  John Case,et al.  Control Structures in Hypothesis Spaces: The Influence on Learning , 1997, EuroCOLT.

[8]  Rusins Freivalds,et al.  Inductive Inference and Computable One-One Numberings , 1982, Math. Log. Q..

[9]  J. Ersov.  Theorie der Numerierungen II , 1973 .

[10]  Martin Kummer.  A Learning-Theoretic Characterization of Classes of Recursive Functions , 1995, Inf. Process. Lett..

[11]  Gregory A. Riccardi.  The Independence of Control Structures in Abstract Programming Systems , 1981, J. Comput. Syst. Sci..

[12]  Louise Hay.  Isomorphism types of index sets of partial recursive functions , 1966 .

[13]  Jr. Hartley Rogers.  Theory of Recursive Functions and Effective Computability , 1969 .

[14]  Thomas Zeugmann,et al.  Characterization of language learning front informant under various monotonicity constraints , 1994, J. Exp. Theor. Artif. Intell..

[15]  Paul Young,et al.  An introduction to the general theory of algorithms , 1978 .

[16]  Manuel Blum,et al.  A Machine-Independent Theory of the Complexity of Recursive Functions , 1967, JACM.

[17]  James S. Royer.  A Connotational Theory of Program Structure , 1987, Lecture Notes in Computer Science.

[18]  H. Gordon Rice,et al.  On completely recursively enumerable classes and their key arrays , 1956, Journal of Symbolic Logic.