[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ skip to main content
10.1145/800169.805429acmconferencesArticle/Chapter ViewAbstractPublication PagesstocConference Proceedingsconference-collections
Article
Free access

Computability over arbitrary fields

Published: 05 May 1969 Publication History

Abstract

In most attempts to make precise the concept of a computable function, or decidable predicate, over a field F, it is considered necessary that the elements of F should be in some sense effectively describable, and hence that F itself should be countable. This is the attitude taken in the study of computable fields (see Rabin1).
Our proposed definition of computability over arbitrary fields is based on the Shepherdson - Sturgis2 concept of an unlimited register machine.

References

[1]
Rabin, M.O. "Computable algebra, general theory and theory of computable fields", Trans. Amer. Math. Soc, 87, (1960), 341-360.
[2]
Shepherdson, J.C. & Sturgis, H.E. "Computability of recursive functions", J. Assoc. Comp. Mach., 10, (1963), 217-255.
[3]
Gallaire, H., Gray, J.N., Harrison, M.A. & Herman, G.T. "Infinite linear sequential machines", Journal of Computer and System Sciences, 2, (1968), 381-419.
[4]
Tarski, A. A decision method for elementary algebra and geometry, 2nd edition, Berkeley and Los Angeles, 1951, VI + 63 pp.

Recommendations

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image ACM Conferences
STOC '69: Proceedings of the first annual ACM symposium on Theory of computing
May 1969
267 pages
ISBN:9781450374781
DOI:10.1145/800169
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 05 May 1969

Permissions

Request permissions for this article.

Check for updates

Qualifiers

  • Article

Acceptance Rates

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

Upcoming Conference

STOC '25
57th Annual ACM Symposium on Theory of Computing (STOC 2025)
June 23 - 27, 2025
Prague , Czech Republic

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • 0
    Total Citations
  • 242
    Total Downloads
  • Downloads (Last 12 months)34
  • Downloads (Last 6 weeks)5
Reflects downloads up to 21 Dec 2024

Other Metrics

Citations

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Login options

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media