Question

Which of the following statements is true?

a-PDA accepting by final state is more powerful than PDA accepting by empty stack.
b-PDA accepting by final state is less powerful than PDA accepting by empty stack.
c-PDA accepting by final state is equally powerful as PDA accepting by empty stack.
d-PDA accepting by final state is incomparable to PDA accepting by empty stack.

Answer 1

A Pushdown Automaton (PDA) accepting by final state is equally powerful as a PDA accepting by empty stack. Both can recognize the same class of languages, the context-free languages, and can be converted to each other, proving their equivalence.

Step-by-step explanation:

The correct answer to the question is:

c- PDA accepting by final state is equally powerful as PDA accepting by empty stack.

Whether a Pushdown Automaton (PDA) accepts by a final state or by emptying its stack does not change its computational power. Both acceptance methods are capable of recognizing the same class of languages, which are the context-free languages. There are constructions to convert a PDA that accepts by final state to one that accepts by empty stack and vice versa, thus proving their equivalence in terms of the languages they can recognize.