IDEAS home Printed from https://ideas.repec.org/a/sae/envirb/v40y2013i4p576-594.html
   My bibliography  Save this article

Tractable Shape Grammars

Author

Listed:
  • Kui Yue

    (Microsoft, Redmond, WA 98052, USA)

  • Ramesh Krishnamurti

    (Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA)

Abstract

In this paper we explore the theoretical basis for a concept of ‘computation-friendly’ shape grammars, through a formal examination of tractability of the grammar formalism. Although a variety of shape grammar definitions have evolved over time, it is possible to unify these to be backwards compatible. Under this unified definition, a shape grammar can be constructed to simulate any Turing machine from which it follows that: A shape grammar may not halt; its language space can be exponentially large; and in general, its membership problem is unsolvable. Moreover, parametric subshape recognition is shown to be NP. This implies that it is unlikely, in general, to find a polynomial-time algorithm to interpret parametric shape grammars, and that more pragmatic approaches need to be sought. Factors that influence the tractability of shape grammars are identified and discussed.

Suggested Citation

  • Kui Yue & Ramesh Krishnamurti, 2013. "Tractable Shape Grammars," Environment and Planning B, , vol. 40(4), pages 576-594, August.
    • Handle: RePEc:sae:envirb:v:40:y:2013:i:4:p:576-594
    DOI: 10.1068/b38227
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1068/b38227
    Download Restriction: no
    File URL: https://libkey.io/10.1068/b38227?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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:sae:envirb:v:40:y:2013:i:4:p:576-594. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.