IDEAS home Printed from https://ideas.repec.org/p/wop/safiwp/00-09-051.html
   My bibliography  Save this paper

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

Author

Listed:
  • Jarkko Kari
  • Cristopher Moore

Abstract

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.

Suggested Citation

  • Jarkko Kari & Cristopher Moore, 2000. "New Results on Alternating and Non-Deterministic Two-Dimensional Finite-State Automata," Working Papers 00-09-051, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:00-09-051
    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

    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: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). 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.