I was asked the next question in my homework assignment: I just want to make sure that I fully understand what it is that's required of me. Am I asked to find an algorithm which decides if the language that's accepted by the PDA is finite? And if not, then what is it? Any initial intuition?
**I don't need help with answering it, just understanding the question. I'm asked to show an algorithm that given a PDA $A$ decides whether there exists a word $w$ that's accepted by the PDA for which there exists a decomposition $w=uvxyz$ that satisfies that the length of $vy$ is atleast 1 and $u(v^i)x(y^i)z$ is accepted by the PDA for every $i\ge0$.