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Closure properties of CFL Part - 2

Assume the st...

Question

Assume the statements $S_{1} a n d S_{2}$ given as:
$S_{1}$ : Given a context free grammer, there exists an algorithm for determining whether L(g) is infinite.
$S_{2}$ : There exists an algorithm to determine whether two context free grammars generate the same language.
Which of the following is true?

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Solution

The proof of $S_{1}$ can be seen in various book of theory category undecidable so a contradiction to this assumption

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