$1^{st}$ Question:

One$-$way vs$.$ Two$-$way. We wish to construct a Turing Machine

$M=(Q,,,,s,q_{\text{a}\text{c}\text{c}\text{e}\text{p}\text{t}},q_{\text{r}\text{e}\text{j}\text{e}\text{c}\text{t}})$

that decides the language

For which, if any, of the following machine models does $M$ decide $L?$ Explain your answers.

$($a$)M$ is a standard machine with a one$-$way infinite tape.

$($b$)M$ has a two$-$way infinite tape.