IDEAS home Printed from https://ideas.repec.org/p/wop/safiwp/01-12-083.html
   My bibliography  Save this paper

Computation with Switching Map Systems: Nonlinearity and Computational Complexity

Author

Listed:
  • Yuzuru Sato
  • Makoto Taiji
  • Takashi Ikegami

Abstract

A dynamical-systems-based model of computation is studied. We demonstrate the computational ability of nonlinear mappings. There exists a switching map system with two types of baker's map to emulate any Turing machine. Taking non-hyperbolic mappings with second-order nonlinearity (e.g., the HŽnon map) as elementary operations, the switching map system becomes an effective analog computer executing parallel computation similar to MRAM. Our results show that, with an integer division map similar to the Gauss map, it has PSPACE computational power. Without this, we conjecture that its computational power is between class RP and PSPACE. Unstable computation with this system implies that there would be a trade-off principle between stability of computation and computational power.

Suggested Citation

  • Yuzuru Sato & Makoto Taiji & Takashi Ikegami, 2001. "Computation with Switching Map Systems: Nonlinearity and Computational Complexity," Working Papers 01-12-083, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:01-12-083
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below 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.

    More about this item

    Keywords

    Smale's horseshoe; HŽnon map; symbolic dynamics; non-hyperbolicity; computational complexity;

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wop:safiwp:01-12-083. 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). General contact details of provider: http://edirc.repec.org/data/epstfus.html .

    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.

    We have no references for this item. You can help adding them by using 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.