Difference between Left Factoring and Left Recursion

Question

What is the difference between Left Factoring and Left Recursion ? I understand that Left factoring is a predictive top down parsing t

Answer 1

Left Recursion: A grammar is left recursive if it has a nonterminal A such that there is a derivation A -> Aα | β where α and β are sequences of terminals and nonterminals that do not start with A.

While designing a top down-parser, if the left recursion exist in the grammar then the parser falls in an infinite loop, here because A is trying to match A itself, which is not possible. We can eliminate the above left recursion by rewriting the offending production. As-

A -> βA'

A' -> αA' | epsilon

Left Factoring: Left factoring is required to eliminate non-determinism of a grammar. Suppose a grammar, S -> abS | aSb

Here, S is deriving the same terminal a in the production rule(two alternative choices for S), which follows non-determinism. We can rewrite the production to defer the decision of S as-

S -> aS'

S' -> bS | Sb

Thus, S' can be replaced for bS or Sb