I have the following Turing machine: A 2R-3L-TM is similar to a standard TM with the change in which the head can only move either 3 cells to the left or 2 cells to the right (those are the only possible moves). and I want to prove equivalence between 2R-3L-TM and standard TMs (one tape and the head can move single cell right or left only). I only want to prove one side, meaning that for every standard TM M_1, there is a $2R-3L-TM, M_2, s.t L\left(M_1\right)=L(M_2)$. I started the proof on the right side but not sure how to prove the triple left side, my proof so far:
Let M2, a TM with 2R-3L, a set of states Q and transition function \delta. Let us define an equal standard machine, M2. We would do so by describing how TM M1 works in the implementation level:
- If M1 moves to the right, do the same for M2 however mark the position with ‘ * ‘ transition to a new state at which the machine always moves to the right and then transitions to the original target of the RR transition
- If M1 moves to the left...
How can I continue my proof and is my proof for the right side correct?