decidability

Question

INFINITE_PDA = {<M> | M is a PDA and L(M) is an infinite language } . Then -

a) INFINITE_PDA is undecidable.

b) INFINITE_PDA is decidable.

c) INFINITE_PDA is recursive enumerable.

d) INFINITE_PDA is Turing co-recognizable.

Answer 1

1. Make variables vertices of the graph. 
2. An edge from $V_{i}$ to $V_{j}$ iff there exists a production having $V_{i}$ at the left & $V_{j}$ at the right for the grammar of $L(M)$.
3. If there is a cycle in the graph $L(M)$ is infinite, otherwise not. 

Hence, IMO given language is decidable.

Comments

@Aghori , can you give the whole explanation of the above question.

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Given language (say A) is a set of PDAs having infinite language. Now tell whether given language (A) is decidable or not.

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A is decidable