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The membership problem for the language generated by a grammar

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The problem can described like this: Given a grammar and a string, is the string an element of the language generated by the grammar? There exist corresponding algorithms for certain classes of grammars, e.g., for context-free grammars, in which case the parsing problem turns out to be an algorithmic problem, thus. While the parsing problem, in a narrow sense, focuses indeed on the membership aspect, it may be understood more broadly to cover the richer algorithmic problem of what a parser is supposed to that, which include recovery of the syntactical structure of the input in the form of a syntax tree.

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