Example
The context free grammar
- A → A + A | A − A | a
is ambiguous since there are two leftmost derivations for the string a + a + a:
| A | → A + A | A | → A + A | ||
| → a + A | → A + A + A (First A is replaced by A+A. Replacement of the second A would yield a similar derivation) | ||||
| → a + A + A | → a + A + A | ||||
| → a + a + A | → a + a + A | ||||
| → a + a + a | → a + a + a |
As another example, the grammar is ambiguous since there are two parse trees for the string a + a − a:
The language that it generates, however, is not inherently ambiguous; the following is a non-ambiguous grammar generating the same language:
- A → A + a | A − a | a
Read more about this topic: Ambiguous Grammar
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