Finite State Brainfuck

Finite State Brainfuck is a brainfuck variant that is equivalent to a finite state machine, due to being a read only Turing Machine.

Instructions

Brainfuck without + and - instructions, however the tape should have the values inputted initially:

Program example

0 5 1 8 234 13 9 7 7 2           <-- (== TAPE, but rest is filled w/ 0s after this initial input)
>[.>]                            <-- (Program)

Instructions list and ,

Instructions are

> < [ ] .

Allowing use of the input instruction:

,

Will make it more powerful (in some sense), but still in the same class as a FSM.

Perhaps this idea could be extended in some ways while keeping the FSM status of the language, like say

{ ... }                      <--- Unconditional Infinite Loop for ... (or even zeno infinite loop?)

and if that changes the language's class.