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Recursive descent with backtracking is a technique that determines which production to use by trying each production in turn. Recursive descent with backtracking is not limited to LL(k) grammars, but is not guaranteed to terminate unless the grammar is LL(k).
LL parsers may be table-based, [citation needed] i.e. similar to LR parsers, but LL grammars can also be parsed by recursive descent parsers. According to Waite and Goos (1984), [ 9 ] LL( k ) grammars were introduced by Stearns and Lewis (1969).
For every LL(k) grammar, a structurally equivalent strong LL(k) grammar can be constructed. [6] The class of LL(k) languages forms a strictly increasing sequence of sets: LL(0) ⊊ LL(1) ⊊ LL(2) ⊊ …. [7] It is decidable whether a given grammar G is LL(k), but it is not decidable whether an arbitrary grammar is LL(k) for some k.
A formal grammar that contains left recursion cannot be parsed by a LL(k)-parser or other naive recursive descent parser unless it is converted to a weakly equivalent right-recursive form. In contrast, left recursion is preferred for LALR parsers because it results in lower stack usage than right recursion.
Context-free languages are a category of languages (sometimes termed Chomsky Type 2) which can be matched by a sequence of replacement rules, each of which essentially maps each non-terminal element to a sequence of terminal elements and/or other nonterminal elements.
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It is also possible to build LL parsers and LR parsers from parsing expression grammars, [citation needed] with better worst-case performance than a recursive descent parser without memoization, but the unlimited lookahead capability of the grammar formalism is then lost. Therefore, not all languages that can be expressed using parsing ...
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