We can prove that for any pushdown automaton $($PDA$),$ there is an equivalent Turing machine with two tapes that recognizes the same language as the PDA. Basically, the equivalent Turing machine simulates every transition of the PDA. It uses the first tape to store an input string $($read from but does not write to the first tape$).$ It uses the second tape to simulate the PDA stack with the current tape symbol as the current top stack symbol. $$ To simplify the discussion, we assume that the PDA has only one copy at any time when reading an input string. $$ To simplify the discussion, we assume that the input alphabet