# A push down automaton that recognize exponential strings

How can I describe a Push Down Automaton that recognize the language $P=\{a^{2^n} | n \geq 0 \}$?

My approach

I know that the language can be described by a Turing Machine, but how i can the stack recognize that language?

• This is impossible. You can show it is not context-free by applying the Pumping Lemma. – Hendrik Jan Oct 1 '17 at 14:13
• Existence of a TM accepting a language $L$ does not guarantee existence of a PDA accepting this language. Please look here. – fade2black Oct 1 '17 at 14:16