Narrow Results

The Siromoney matrix model is a simple and elegant model for describing two-dimensional digital picture languages. The notion of attaching indices to nonterminals in a generative grammar, introduced and investigated by Aho. is considered in the vertical phase of a Siromoney matrix grammar (SMG). The advantage of this study is that the new model retains the simplicity and elegance of SMG but increases the generative power and enables us to describe pictures not generable by SMG. Besides certain closure properties and hierarchy results. applications of these two-dimensional grammars to describe tilings, polyominoes, distorted patterns and parquet deformations are studied.

In this paper, we will introduce some variations of tree adjoining grammars which generate the sets of quadtrees as their languages and investigate their effectiveness to describe the sets of digital images. In those variations, two types of parallel operations, multicomponent and multifoot adjoining, will be introduced. Both of them are quite different parallelisms from ordinary ones (such as Indian parallelism of grammars, or L-systems).

The Siromoney matrix model is a simple and elegant model for describing two-dimensional digital picture languages. The notion of attaching indices to nonterminals in a generative grammar, introduced and investigated by Aho, is considered in the vertical phase of a Siromoney matrix grammar (SMG). The advantage of this study is that the new model retains the simplicity and elegance of SMG but increases the generative power and enables us to describe pictures not generable by SMG. Besides certain closure properties and hierarchy results, applications of these two-dimensional grammars to describe tilings, polyominoes, distorted patterns and parquet deformations are studied.