Read-only Turing machine

A read-only Turing machine or Two-way deterministic finite-state automaton (2DFA) is class of models of computability that behave like a standard Turing machine and can move in both directions across input, except cannot write to its input tape. The machine in its bare form is equivalent to a Deterministic finite automaton in computational power, and therefore can only parse a regular language.

We define a standard Turing machine by the 9-tuple

${\displaystyle M=(Q,\Sigma ,\Gamma ,\vdash ,\_,\delta ,s,t,r)}$ where

So given initial state ${\displaystyle q}$ reading symbol ${\displaystyle a}$, we have a transition defined by ${\displaystyle \delta (q,a)=(q_{2},a_{2},d)}$ which replaces ${\displaystyle a}$ with ${\displaystyle a_{2}}$, transitions to state ${\displaystyle q_{2}}$, and moves the "read head" in direction ${\displaystyle d}$ (left or right) to read the next input. In our 2DFA read-only machine, however, ${\displaystyle a=a_{2}}$ always.

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