On computability by certain classes of restricted turing machines

The theory of abstract machines has been well developed for the finite automaton [RS] and the Turing machine [D]. More recently, machines intermediate in computing power between the above two classes of machines have been investigated. These machines have some form of unbounded memory, thus giving them more potential computing ability than the finite automata, but the access to the unbounded memory is restricted in some way so that they do not have the full power of a Turing machine. The two forms of restricted unbounded memory we shall consider here are the counter and the pushdown store.