Abstract
Phrase structure grammars, in which non-terminal symbols on the left side of a production can be rewritten by the string on the right side, together with their Chomsky hierarch classification, are familiar to computer scientists. But, these grammars are most effective only to generate, and parse, strings.
In this paper, we introduce a new kind of grammar in which the right side of the production is simply appended to the intermediate structure in such a way that the left side becomes its “neighborhood” in the new structure.
This permits the grammatical definition of many different kinds of “n-dimensional” discrete structures. Several examples are given.
Moreover, these grammars yield a formal theory grounded in antimatroid closure spaces. For example, we show that restricted neighborhood expansion grammars capture the essence of finite state and context free phrase structure grammars.
Research supported in part by DOE grant DE-FG05-95ER25254.
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Pfaltz, J.L. (2000). Neighborhood Expansion Grammars. In: Ehrig, H., Engels, G., Kreowski, HJ., Rozenberg, G. (eds) Theory and Application of Graph Transformations. TAGT 1998. Lecture Notes in Computer Science, vol 1764. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46464-8_3
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DOI: https://doi.org/10.1007/978-3-540-46464-8_3
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