# What is the class of automata with stack and unlimited amount of memory, addressable only by immediates?

Let's assume we've got an automata with infinite stack ($$s_n \epsilon \mathbb{Z}$$) and infinite amount of "registers", but no arbitrary memory access whatsoever and it's data is separated from code.

I'm sure that this is at least pushdown automata, but I'm not entirely sure can we pull this machine up to the linear bounded automation in the current state of art. The upper bound is obviously the Turing machine (because pushdown automata with one additional stack has the same capabilities as the Turing machine).

The only way to store data using this automata would be either pushing it onto the stack (push #3 - push contents of register 3 to the stack, or push 3 - push 3 to the stack), or using mov instruction with at least one register specification (mov #1, 1 register 1 = 1, mov #2, #1, register 2 = register 1). We can also assume that loop operations are there, along with addition or subtraction.

Let's assume only allowed operations are while-like loops, addition and subtraction.

The question(s) are:

• What is the class of this automata?
• If this automata isn't a linear bounded automation or a Turing machine, what needs to be done for it to become one except the following:
Edit: Let's define register (in this context) as memory cell, $$r_n$$ where $$n \epsilon \mathbb{N} \wedge r_n \epsilon \mathbb{Z}$$, that is addressable only using constant stated explicitly, eg. $$r_7$$ (invalid: $$r_{r_3 + 2}$$).