ambiguity

Question

$E→E−T ∣ T$

$T→T/F ∣ F$

$F→(E) ∣ id$

(E is the start symbol)

This grammar is unambiguous but shouldn't it be ambiguous because it has left recursion?

Comments

There is no relation between ambiguity and left recursion

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unambiguous grammar is left recursive and right-recursive as well, to ensure the dis-ambiguity we see the left associativity and precedence in an ambiguous grammar.

Answer 1

No because there is no relation between ambiguity and left recursion.

Ambiguity means that we can derive two parse tree for same string whereas Left recursion means that the parse tree will grow in leftward direction which will eventually lead to infinite recursion. That is the reason why Left recursive grammars can't be parsed by Top down parsers.

Comments

@yogesh

so ambiguity of a grammar can only be determined by construcing parse tree for a string ?

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Yes if you are able to construct two different parse tree for the same string then that grammar is ambiguous.
Or if the grammar is both left and right recursive than the grammar is also ambiguous.

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@yogesh

left and right recursive or left and right linear ?