Abstract
The concept of Chomsky-grammar is generalized to multi-dimensional arrangement of symbols using multi-graphs the vertices and edges of which are labelled. The question arises in what cases productions preserve partial ordering. Vie give a necessary and sufficient condition for this. Furthermore, it is shown that context-free string grammars are a special case, but this is not true for context-sensitive grammars. Context-sensitive grammars in our definition are related to scattered context grammars.
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Schneider, H.J. (1973). A Necessary and Sufficient Condition for Chomsky-Productions Over Partially Ordered Symbol Sets. In: Deussen, P. (eds) GI. Gesellschaft für Informatik e.V. 2. Jahrestagung. Lecture Notes in Economics and Mathematical Systems, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80732-9_9
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DOI: https://doi.org/10.1007/978-3-642-80732-9_9
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