Abstract
Nivat et al. proposed a class of grammars called puzzle grammars. Such models are suitable for describing and generating connected arrays consisting of unit cells. In this paper, we introduce the stochastic version of puzzle grammars. Conditions for their consistency are given. Although the simplest of puzzle grammars, called basic puzzle grammar, generates a larger class of pictures than regular array grammars, the additional generative power is restricted and it requires considerable effort to write grammars for even pictures whose complexity is not high. We propose a parallel version of the puzzle grammar model which lends itself naturally to the generation of pictures. Several examples are given to illustrate the power of this model. Its stochastic version is presented along with an application to the clustering of syntactic patterns.
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