Date of Original Version

4-2013

Type

Article

Rights Management

The final publication is available at Sage via http://dx.doi.org/10.1068/b38227

Abstract or Description

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.

DOI

10.1068/b38227

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Published In

Environment and Planning B: Planning and Design, 40, 4, 576-594.