Question

Let P be a non-deterministic push-down automation (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. Let the input alphabet of the PDA be Σ.
Let L(P) be the language accepted by the PDA by reading a string and reaching its accepting state. Let N(P) be the language accepted by the PDA by reading a string and emptying its stack. Which of the following statements is TRUE?

Answer 1

In NPDA may have a dead configuration i.e. transition for every alphabet not present from this state. So it is not necessary that both L(P) and N(P) are represents ${\sum }^{\ast }$.