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 Factoring is a grammar transformation technique. It consists in "factoring out" prefixes which are common to two or more productions.

For example, going from:

A → α β | α γ

to:

A → α A'

A' → β | γ

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Left Recursion is a property a grammar has whenever you can derive from a given variable (non terminal) a rhs that begins with the same variable, in one or more steps.

For example:

A → A α

or

A → B α

B → A γ

There is a grammar transformation technique called Elimination of left recursion, which provides a method to generate, given a left recursive grammar, another grammar that is equivalent and is not left recursive.

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The relationship/confusion between both terms probably derives from the fact that both transformation techniques may need to be applied to a grammar before being able to derive a predictive top down parser for it.