A quetue automaton is like a push$-$down automaton except that the stack is replaced b$)$ a queue. A queue is a tape allowing symbols to be written only on the left$-$hand and and read only at the right$-$hand end. Each write operation $($we$\text{'}$ll call it a pabh$)$ adds a symbol to the left$-$hand end of the queue and each read operation $($well$)$ call it a pull$)$ reads and removes a symbol at the right$-$hand end. As with a PDA, the input is placed on a separate read$-$only input tape, and the head on the input tape can move only from left to right. The input tape contains a cell with a blank symbol following the input, so that the end of the input can be detected. A queue automaton accepts its input by entering a special accept state at any time. Show that a language can be recognized by a deterministic queue automaton iff the language is Turing$-$recognizable.