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Some independence results for control structures in complete numberings

Published online by Cambridge University Press:  12 March 2014

Sanjay Jain  and
Jochen Nessel
Sanjay Jain
Affiliation:
National University of Singapore, School of Computing, Singapore. 119260, Singapore, E-mail: sanjay@comp.nus.edu.sg
Jochen Nessel
Affiliation:
Universität Kaiserslautern, FB Informatik, Postfach 3049. 67653. Kaiserslautern, Germany, E-mail: nessel@informatik.uni-kl.de
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Abstract

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 Eršov.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 1 , March 2001 , pp. 357 - 382
Copyright
Copyright © Association for Symbolic Logic 2001

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References

REFERENCES

[1]Angluin, D., Inductive inference of formal languages from positive data, Information and Control, vol. 45 (1980), pp. 117–135.CrossRefGoogle Scholar
[2]Blum, M., A machine independent theory of complexity of recursive functions, Journal of the ACM, vol. 14 (1967), pp. 322–336.CrossRefGoogle Scholar
[3]Case, J., Jain, S., and Suraj, M., Control structures in hypothesis spaces: The influence on learning, Proceedings of the Third European Conference on Computation Learning Theory (Ben-David, S., editor), Lecture Notes in Artificial Intelligence, Springer-Verlag, 1997, pp. 286–300.CrossRefGoogle Scholar
[4]Eršov, Yu. L., Theorie der Numerierungen 1, Zeitschrift für Mathenatische Logik und Grundlagen der Mathematik, vol. 19 (1973), pp. 289–388.CrossRefGoogle Scholar
[5]Freivalds, R.et al., How inductive inference strategies discover their errors. Information and Control, vol. 118 (1995), pp. 208–226.Google Scholar
[6]Freivalds, R., Kinber, E., and Wiehagen, R., Inductive inference and computable one-one numberings, Zeitschrift für Mathenatische Logik und Grundlagen der Mathematik, vol. 28 (1982), pp. 463–479.CrossRefGoogle Scholar
[7]Hay, L., Isomorphism types for index sets of partial recursive functions, Proceedings of the American Mathematical Society, vol. 16, 1966, pp. 106–110.CrossRefGoogle Scholar
[8]Kummer, M., A learning-theoretic charactarization of classes of recursive functions, Information Processing Letters, vol. 54 (1995), pp. 205–211.CrossRefGoogle Scholar
[9]Lange, S. and Zeugmann, T., Language learning in dependence of the space of hypothesis. Proceedings of the 6th Annual ACM Conference on Computational Learning Theory (New York), ACM Press, 1993, pp. 127–136.CrossRefGoogle Scholar
[10]Lange, S. and Zeugmann, T.Characterization of language learning under various monotonicity constraints, Journal of Experimental and Theoretical Artificial Intelligence, vol. 6 (1994), pp. 73–94.CrossRefGoogle Scholar
[11]Machtey, M. and Young, P., An introduction to the general theory of algorithms, New York, 1978.Google Scholar
[12]MAlčev, A. I., Algorithms and recursive functions, Wolthers-Noordhoff Publishing, North Holland, 1970.Google Scholar
[13]Riccardi, G., The independence of control structures in absract programming systems, Ph.D. dissertation, State University of New York at Buffalo, New York, 1980.Google Scholar
[14]Rice, H. G., On completely recursively enumerable classes and their key arrays, this Journal, vol. 21 (1956), pp. 304–308.Google Scholar
[15]Rogers, H. Jr., Theory of recursive functions and effective computabittty, MIT Press, Cambridge, Massachusetts, 1987.Google Scholar
[16]Royer, J. S., A connotational theory of program structure, Lecture Notes in Computer Science, no. 273, Springer-Verlag, Berlin, 1987.Google Scholar