Advanced Search
MyIDEAS: Login

Iteration, Inequalities, and Differentiability in Analog Computers

Contents:

Author Info

  • Manuel Lameiras Campagnolo
  • Cristopher Moore
  • José Félix Costa
Registered author(s):

    Abstract

    Shannon's General Purpose Analog Computer (GPAC) is an elegant model of analog computation in continuous time. In this paper, we consider whether the set G of GPAC-computable functions is closed under iteration, that is, whether for any function f(x) 2 G there is a function F(x; t) 2 G such that F(x; t) = f t (x) for non-negative integers t. We show that G is not closed under iteration, but a simple extension of it is. In particular, if we relax the definition of the GPAC slightly to include unique solutions to boundary value problems, or equivalently if we allow functions x k f(x) that sense inequalities in a differentiable way, the resulting class, which we call G + fk, is closed under iteration. Furthermore, G + k includes all primitive recursive functions, and has the additional closure property that if T(x) is in G +k, then any function of x computable by a Turing machine in T(x) time is also.

    Download Info

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below under "Related research" whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Bibliographic Info

    Paper provided by Santa Fe Institute in its series Working Papers with number 99-07-043.

    as in new window
    Length:
    Date of creation: Jul 1999
    Date of revision:
    Handle: RePEc:wop:safiwp:99-07-043

    Contact details of provider:
    Postal: 1399 Hyde Park Road, Santa Fe, New Mexico 87501
    Web page: http://www.santafe.edu/sfi/publications/working-papers.html
    More information through EDIRC

    Related research

    Keywords: Analog computation; recursion theory; iteration; differentially algebraic functions; primitive recursive functions;

    This paper has been announced in the following NEP Reports:

    References

    No references listed on IDEAS
    You can help add them by filling out this form.

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:wop:safiwp:99-07-043. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Thomas Krichel).

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.