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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.
For a general method, see removing left recursion. A simple example for left recursion removal: The following production rule has left recursion on E E -> E '+' T E -> T This rule is nothing but list of Ts separated by '+'. In a regular expression form T ('+' T)*. So the rule could be rewritten as E -> T Z Z -> '+' T Z Z -> ε Now there is no ...
Depending on the presence of empty derivations, a LL(1) grammar can be equal to a SLR(1) or a LALR(1) grammar. If the LL(1) grammar has no empty derivations it is SLR(1) and if all symbols with empty derivations have non-empty derivations it is LALR(1). If symbols having only an empty derivation exist, the grammar may or may not be LALR(1). [12]
An) then the grammar will grow exponentially. If the ordering is reversed (An, An-1, .. A1) the grammer is left untouched since every direct left corner already precedes it's definition. A good article on this and alternative algorithms for removing left recursion is Removing Left Recursion from Context-Free Grammars.
Any context-free grammar can be transformed into an equivalent grammar that has no left recursion, but removal of left recursion does not always yield an LL(k) grammar. A predictive parser runs in linear time. Recursive descent with backtracking is a technique that determines which production to use by trying
For example, a grammar for a context-free language is left recursive if there exists a non-terminal symbol A that can be put through the production rules to produce a string with A (as the leftmost symbol). [2] [3] All types of grammars in the Chomsky hierarchy can be recursive and it is recursion that allows the production of infinite sets of ...
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Obtain an intermediate grammar by replacing each rule A → X 1... X n. by all versions with some nullable X i omitted. By deleting in this grammar each ε-rule, unless its left-hand side is the start symbol, the transformed grammar is obtained. [4]: 90 For example, in the following grammar, with start symbol S 0, S 0 → AbB | C B → AA | AC ...