IDEAS home Printed from
MyIDEAS: Login to save this paper or follow this series

New Results on Alternating and Non-Deterministic Two-Dimensional Finite-State Automata

  • Jarkko Kari
  • Cristopher Moore
Registered author(s):

    We resolve several long-standing open questions regarding the power of various types of finite-state automata to recognize "picture languages," i.e. sets of two-dimensional arrays of symbols. We show that the languages recognized by 4-way alternating finite-state automata (AFAs) are incomparable to the so-called tiling recognizable languages. Specifically, we show that the set of acyclic directed graphs is AFA-recognizable but not tiling recognizable, while the set of non-acyclic directed graphs is tiling recognizable but not AFA-recognizable. More generally, the complement of an AFA-recognizable language is tiling recognizable, and therefore the AFA-recognizable languages are not closed under complement. We also show that the set of languages recognized by 4-way NFAs is not closed under complement, and that NFAs are more powerful than DFAs, even for languages over one symbol.

    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.

    Paper provided by Santa Fe Institute in its series Working Papers with number 00-09-051.

    in new window

    Date of creation: Sep 2000
    Date of revision:
    Handle: RePEc:wop:safiwp:00-09-051
    Contact details of provider: Postal: 1399 Hyde Park Road, Santa Fe, New Mexico 87501
    Web page:

    More information through EDIRC

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

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

    When requesting a correction, please mention this item's handle: RePEc:wop:safiwp:00-09-051. 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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.