Skip to main content
SpringerLink
Log in

The non-renameability of honesty classes

Die Nicht-Umbenennbarkeit der gutartigen Funktionenklassen

  • Published:
Computing Aims and scope Submit manuscript

Abstract

An important result in the theory of complexity classes is the naming theorem of E. M. McCreight, which states that the system of complexity classes can be renamed uniformly by a measured set of names. Our investigation of honesty classes shows that for these classes the analogous assertion is false. No measured transformation of programs renames correctly all honesty classes.

Zusammenfassung

Ein wichtiges Ergebnis der Komplexitätstheorie ist der Umbenennungssatz von E. M. McCreight, der besagt, daß es einen Algorithmus σ gibt, der alle Namen ϕi des Systems der Komplexitätsklassen in neue Namen ϕσ(i) überführt, derart, daß die neuen Namen die Schrittmaßbedingung „λi,n,m[ϕσ(i)(n)≦m] entscheidbar” erfüllen. Unsere Untersuchung der „gutartigen Funktionenklassen” zeigt, daß ein entsprechender Umbenennungsalgorithmus für diese Klassen nicht existiert.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bass, L.: Hierarchies based on computational complexity and irregularities of class determining measured sets. Doctoral thesis, Purdue University, 1970.

  2. Bass, L., Young, P.: Ordinal hierarchies and naming complexity classes. J. ACM20, 668–686 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  3. Blum, M.: A machine independent theory of the complexity of recursive functions. J. ACM14, 322–336 (1967).

    Article  MathSciNet  MATH  Google Scholar 

  4. Borodin, A.: Complexity classes of recursive functions and the existence of complexity gaps. J. ACM19, 158–174 (1972).

    Article  MATH  Google Scholar 

  5. Constable, R. L.: The operator gap. J. ACM19, 175–183 (1972).

    Article  MathSciNet  MATH  Google Scholar 

  6. van Emde Boas, P.: A comparison of the properties of complexity classes and honesty classes, in: Automata, Languages and Programming, Proc. Symp. Inst. Rech. Informatique Automatique (IRIA), p. 391–396. Rocquencourt: North Holl. Publ. Comp. 1973.

    Google Scholar 

  7. van Emde Boas, P.: Abstract resource-bound classes. Doctoral thesis, Univ. of Amsterdam, 1974.

  8. McCreight, E.: Classes of computable functions defined by bounds on computation. Doctoral thesis, Carnegie Mellon University, 1969. (See also the joint paper with A. Meyer under the same title presented at the First ACM Symp. on the Theory of Computing, 1969, p. 79–88.)

  9. Meyer, A., Moll, R.: Honest bounds for complexity classes of recursive functions. Proj. MAC, Technical Report, April 1972, MIT, Cambridge (Mass.).

    Book  MATH  Google Scholar 

  10. Moll, R., Meyer, A.: Honest bouds for complexity classes of recursive functions. J.S.L.39, 127–138 (1974).

    MathSciNet  MATH  Google Scholar 

  11. Moll, R.: Complexity classes of recursive functions. Report MAC TR 110, June 1973, MIT Cambridge (Mass.), doctoral thesis.

    Google Scholar 

  12. Rogers, H., Jr.: Gödel numbering of partial recursive functions. J.S.L.23, 331–341 (1958).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisch Instituut, Univ. of Amsterdam, Roetersstraat 15, 1005, Amsterdam, Netherlands

    P. van Emde Boas

  2. Mathematisch Centrum, 2e Boerhaavestraat 49, 1005, Amsterdam, Netherlands

    P. van Emde Boas

Authors
  1. P. van Emde Boas
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This paper is registered as Mathematical Centre Report ZW 18/73.

Rights and permissions

Reprints and permissions

About this article

Cite this article

van Emde Boas, P. The non-renameability of honesty classes. Computing 14, 183–193 (1975). https://doi.org/10.1007/BF02242317

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02242317

Key words

Search

Navigation