Let P be a non-deterministic pushdown automaton (NPDA) with exactly one state, q, and exactly one symbol, Z, in its stack alphabet. State q is both the starting as well as the accepting state of the PDA. The stack is initialized with one Z before the start of the operation of the PDA. ... but L(P) is not necessarily ∑* Both L(P) and N(P) is necessarily ∑* Neither L(P) nor N(P) are necessarily ∑*

given a pushdown automata that receives L by getting to an accepting state, how can a pushdown automata be built, so that it accepts L*? (might use a “double bottom” if needed)?? i don’t know how to solve it and would appreciate any kind of help! studying for exam and must learn how to solve it