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1.)    Consider the following grammar in which S, A, and B are nonterminal symbols and S...

1.)    Consider the following grammar in which S, A, and B are nonterminal symbols and S is the start symbol.

S → 1A | 0B

A → A0 | 1B

B → 10A| 1

Show that the grammar is ambiguous by showing two parse trees for the sentence 1110110 using leftmost derivation.

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Answer #1

In the leftmost derivation of a language the leftmost non-terminal is replaced at every step to obtain the required string.

The string 1110110 can be obtained by two leftmost derivations which are as follows:

1.

S-) IA (The leftmost non-terminal is A.) IA → 1 1 B (The leftmost non-terminal is B.) 11B → 1 1 10A (The leftmost non-termina

The parse tree of the above presented derivation is as follows:

2.

S1A (The leftmost non-terminal is A.) 1A → 1A0(The leftmost non-terminal is A.) 1A0 11B0 (The leftmost non-terminal is B.) 11

The parse tree for the above presented representation is as follows:

1 1 0 1 1 1

Since there are two different parse trees possible using the left-most derivation for the same input string therefore, the given grammar is ambiguous.

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