Let G = ({S}, {a, b} R, S) be a context free grammar where the rule set R is S → a S b | SS | ε Which of the following statements is true?
(A)
G is not ambiguous
(B)
There exist x, y, ∈ L (G) such that xy ∉ L(G)
(C)
There is a deterministic pushdown automaton that accepts L(G)
(D)
We can find a deterministic finite state automaton that accepts L(G)
Answer: (C)
Explanation:
An ambiguous grammar can be converted to unambiguous one.
Here we can get grammar in partial GNF form as
S -> ab | abS | aSb | aSbS
We can convert this into GNF too but no need for PDA reasoning so, above grammar is not a ambiguous thus a definite PDA possible
Trick for this is but just deriving 3-4 strings from grammar, we can easily understand its (anbn)* above
expression anbn is in CFL thus closure of DCFG is a DCFG i.e., you can get L = {ε, ab, abab, aabb, aabbab, abaabb, ababab,……}
PDA will push \”a\” until \”b\” is read, start popping \”a\” for the \”b\” read.
If \”a\” is read again from the tape then push only when stack is empty else terminate.
Repeat this until string is read.
Quiz of this Question
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