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Hyperedge replacement (HR) allows to define context-free graph languages, but parsing is NP-hard in the general case. Predictive top-down (PTD) is an efficient, backtrack-free parsing algorithm for subclasses of HR and contextual HR grammars, which has been described and implemented in earlier work, based on a representation of graphs and grammar productions as strings. In this paper, we define PTD parsers for HR grammars by graph transformation rules and prove that they are correct.
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