Abstract. Graphs are a popular data structure, and graph-manipulation programs are common. Graph manipulations can be cleanly, compactly, and explicitly described using graph-rewriting notation.However, when a software developer is persuaded to try graph rewriting, several problems commonly arise. Primarily, it is difficult for a newcomer to develop a feel for how computations are expressed via graph rewriting. Also, graph-rewriting is not convenient for solving all aspects of a problem: better mechanisms are needed for interfacing graph rewriting with other styles of computation. Efficiency considerations and the limited availability of development tools further limit practical use of graph rewriting. The inaccessible appearance of the graph-rewriting literature is an additional hindrance. These problems can be addressed through a combination of "public relations" work, and further research and development, thereby promoting the widespread use of graph rewriting.

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In image analysis, recognition of the primitives plays an important role. Subsequent analysis is used to interpret the arrangement of primitives. This subsequent analysis must make allowance for errors or ambiguities in the recognition of primitives. In this paper, we assume that the primitive recognizer produces a set of possible interpretations for each primitive. To reduce this primitive-recognition ambiguity, we use contextual information in the image, and apply constraints from the image domain. This process is variously termed constraint satisfaction, labeling or discrete relaxation. Existing methods for discrete relaxation are limited in that they assume a priori knowledge of the neighborhood model: before relaxation begins, the system is told (or can determine) which sets of primitives are related by constraints. These methods do not apply to image domains in which complex analysis is necessary to determine which primitives are related by constraints. For example, in music notation, we must recognize which notes belong to one measure, before it is possible to apply the constraint that the number of beats in the measure should match the time signature. Such constraints can be handled by our graph-rewriting paradigm for discrete relaxation: here neighborhood-model construction is interleaved with constraint-application. In applying this approach to the recognition of simple music notation, we use approximately 180 graph-rewriting rules to express notational constraints and semantic-interpretation rules for music notation. The graph rewriting rules express both binary and higher-order notational constraints. As image-interpretation proceeds, increasingly abstract levels of interpretation are assigned to (groups of) primitives. This allows application of higher-level constraints, which can be formulated only after partial interpretation of the image.