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### GATE CSE 1996

Which of the following statements is false?
A
The halting problem for Turing machine is un-decidable
B
Determining whether ambiguity a context free grammar is un-decidable
C
Given two arbitrary context free grammars $${G_1}$$ and $${G_2}$$ whether $$L\left( {{G_1}} \right) = L\left( {{G_2}} \right)$$
D
Given two regular grammars $${{G_1}}$$ and $${{G_2}},$$ it is un-decidable whether $$L\left( {{G_1}} \right) = L\left( {{G_2}} \right)$$

## Explanation

Case (a):
The Halting Problem for TM is un-decidable problem. By un-decidable means no algorithm exist for it.

Case (b):
Ambiguity in a CFG is undecidable. No algorithm can decide if a CFG is ambiguous. By ambiguous means the CFG has two or more derivations for some sentence.

Case (c):
The equivalance problem of CFG's is undecideable. We have no algorithm to decide if two CFG's generate the same language.

Case (d):
The regular sets are a well behaved class of languages. Practically everything about Regular Language is decidable.
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On those following papers in Marks 1
Number in Brackets after Paper Indicates No. of Questions
GATE CSE 2016 Set 1 (1)
GATE CSE 2014 Set 3 (1)
GATE CSE 2012 (1)
GATE CSE 2008 (1)
GATE CSE 1996 (1)

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