Ambiguity is a property of grammar not languages. If every Context Free Grammar G with Language L = L(G) is ambiguous, then L is said to be inherently ambiguous Language. Whereas following grammars are unambiguous: I) First leftmost derivation II) Second leftmost derivationįollowing are some examples of ambiguous grammars: Let us now consider the following grammar:įrom the above grammar String 3*2+5 can be derived in 2 ways: The following are the 2 parse trees generated by left most derivation:īoth the above parse trees are derived from same grammar rules but both parse trees are different. We can create 2 parse tree from this grammar to obtain a string id+id+id : Let us consider this grammar : E -> E+E|id P is a finite set of productions of the form, A -> α, where A is a variable and α ∈ (V ∪ T)* S is a designated variable called the start symbol.ġ. You can also read our previously discussed article on Classification of Context Free Grammars.Ĭontext Free Grammars(CFGs) are classified based on:ĭepending on Number of Derivation trees, CFGs are sub-divided into 2 types:Ī CFG is said to ambiguous if there exists more than one derivation tree for the given input string i.e., more than one Left Most Derivation Tree (LMDT) or Right Most Derivation Tree (RMDT).ĭefinition: G = (V,T,P,S) is a CFG is said to be ambiguous if and only if there exist a string in T* that has more than on parse tree.
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