I want to design a deterministc TM for the $L$ in the title, I've seen before for $$A=\{0,1,X,Y\} \hspace{0.5cm} B=\{0,1,\$\}$$ $A$ is for the input alphabet and $B$ is for the tape alphabet. (Reference : https://www.geeksforgeeks.org/construct-turing-machine-language-l-ww-w-01/)
My question is for an alphabet $A' = \{0,1\}$. Not using a mark for 0 or 1. It is possible to do a DTM? Some references for this i.e. books? Thank you!