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LEFT RECURSION

LEFT RECURSION. LEFT RECURSION. A grammar is said to be left –recursive if it has a non-terminal A such that there is a derivation A =>Aa, for some string a. Consider the grammar: (i) A -> Aa|b. Corresponding grammar without left recursion: A ->bR R->aR|e.

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LEFT RECURSION

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  1. LEFT RECURSION

  2. LEFT RECURSION A grammar is said to be left –recursive if it has a non-terminal A such that there is a derivation A =>Aa, for some string a. Consider the grammar: (i) A -> Aa|b Corresponding grammar without left recursion: A ->bR R->aR|e

  3. We can eliminate immediate left recursion from them by the following technique . First we group the A-productions as : A -> Aa1 | Aa2 | Aa3 |...| Aam | b1 | b2 | b3 |....| bn where no bi begins with an A. Then we replace the A-productions by A -> b1T | b2T | b3T |......| bnT T -> a1T | a2T | a3T |......| amT | e

  4. The above process removes all immediate left recursions but does not remove recursions involving derivations of two or more steps. Consider the grammar: S -> Aa A -> Sb | c.. Here the grammar does not have immediate left recursion .. but has a left recursion because S =>Aa => Sba

  5. In such cases we set a “hierarchy” among non-terminals and implement the following algorithm. • Arrange the non-terminals n some order A1,A2, …An (setting the hierarchy)

  6. 2. for i=1 to n { for j=1 to i-1 { Replace each production of the form Ai -> Ajg by the production Ai->d1g | d2g | ....| dkg where, Aj -> d1 | d2 | d3 |..... | dk are all the current Aj positions } Eliminate the immediate left recursion among the Ai productions }

  7. For the above grammar, S->Aa A->Aab|c After removing immediate left recursion : S->Aa A->cT T->abT|e

  8. LEFT FACTORING Left factoring is a grammar transformation that is useful for producing a grammar suitable for predictive parsing. Basi Idea : When it is not clear which of two alternative productions to use to expand a non-terminal A, we may be able to rewrite the A-productions to defer the decision until we have seen enough of the input to make the right choice.

  9. For example, A->ab1 | ab2 are two A-productions If the input begins with a non-empty string derived from ‘a’ we do not know whether to expand ‘A’ to ‘ab1’ or ‘ab2’ . However , we may defer the decision by expanding A to aB .

  10. Now, we may expand B to b1 or b2 The left factored original expression becomes: A->aB B->b1|b2

  11. END

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