The document discusses ambiguity in context-free grammars. It provides examples of ambiguous grammars, including one where the grammar G with production rules X → X+X | X*X |X|a is shown to be ambiguous because the string "a+a*a" has two different leftmost derivation trees. It then lists four other grammars and briefly states that each one is ambiguous without showing the derivations.

1. Ambiguity in
Context-Free
Grammars
-Sampath Kumar S,
AP/CSE, SECE

2. Ambiguity in Context-Free
Grammars
 If a context free grammar G has more than one
derivation tree for some string w ∈ L(G), it is called
an ambiguous grammar.
 There exist multiple right-most or left-most
derivations for some string generated from that
grammar.
11/21/2017
Sampath Kumar S, AP/CSE, SECE
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3. Problems to discuss:
74. Check whether the grammar G with production rules:
X → X+X | X*X |X|a is ambiguous or not.
Solution:
Let’s find out the derivation tree for the string "a+a*a". It
has two leftmost derivations.
 Derivation 1 −
X → X+X [∵ X → X+X ]
→ a +X [∵ X → a ]
→ a+ X*X [∵ X → X*X ]
→ a+a*X [∵ X → a ]
→ a+a*a [∵ X → a ]
11/21/2017
Sampath Kumar S, AP/CSE, SECE
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4. Problems to discuss:
 Derivation 2 −
X → X*X [∵ X → X*X]
→ X+X*X [∵ X → X+X ]
→ a+ X*X [∵ X → a ]
→ a+a*X [∵ X → a ]
→ a+a*a [∵ X → a ]
As there are two parse trees for a single string
"a+a*a", the grammar G is ambiguous.
11/21/2017
Sampath Kumar S, AP/CSE, SECE
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5. Problems to discuss:
75. Show that the following grammar is ambiguous E
→ id | E+E | E * E | E – E.
76. Show that the following grammar is ambiguous
S → aS|Sa|a.
77. Show that the following grammar is ambiguous
S → aS|aSb|X, X → Xa|a.
78. Show that the following grammar is ambiguous S
→ i C t S | i C t S e S|a, C → a
11/21/2017
Sampath Kumar S, AP/CSE, SECE
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6. Problems to discuss:
75. id+id*id
76. aa
77. aa
78. ibtibtaea
11/21/2017
Sampath Kumar S, AP/CSE, SECE
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7. 11/21/2017
Sampath Kumar S, AP/CSE, SECE
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8. நன்றி
11/21/2017
Sampath Kumar S, AP/CSE, SECE
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