Given a standard Turing Machine with the transition function: δ(q,a)=(p,b,L/R), meaning the machines head reads 'a' then writes 'b' instead of 'a' then moves to state 'p' Given a variant to the previous Turing machine that firstly moves left or right one block, writes 'b' and only then moves to state 'p'. If were at the leftmost position on the tape and we try to move left, the machine would not move and instead write 'b' instead of 'a'. Decide if both of the machines have the same computational power, meaning is it possible to simulate each other or not. if they are not equivalent in computational power, show a language that one recognizes and the other doesn't.
My thought is that they are not equivalent, example, lets take L={aa}. The original machine will get to the right most position and accept and the tape will be bb. On the variant the is a possibility to recognize only L={a} if the only moves left for some reason. Something feels off here and I'm stuck with my intuition, I'll be really glad to hear your thoughts.