Left factoring

. In top-down parsing when it is not clear which production to choose for expansion of a symbol

defer the decision till we have seen enough input.

In general if A αβ₁ | αβ₂

defer decision by expanding A to a A'

we can then expand A' to β₁ or β₂

. Therefore A αβ₁ | αβ₂

transforms to

A α A'

A' β₁ | β₂

Left factoring is a grammar transformation that is useful for producing a grammar suitable for predictive parsing. The basic idea is that when it is not clear which of two or more alternative productions to use to expand a non-terminal A, we defer the decision till we have seen enough input to make the right choice.

In general if A α ß ₁ | α ß ₂ , we defer decision by expanding A to a A'.

and then we can expand A ' to ß₁ or ß₁

Therefore A α ß₁ | α ß₂ transforms to

A α A'

A ' ß₁ | ß₂