$15\mathrm{.}1$ A Two$-$Way DFA

Let M be a $2-$way DFA with alphabet $\{$a$,$ b$\},$ state set $\{$i$,$ p$,$ f$\},$ start state i$,$ final state set $\{$f$\},$ and transition function $\backslash$delta $($i$,$ a$)=($p$,$ L$),\backslash$delta $($i$,$ b$)=($f$,$ R$),\backslash$delta $($p$,$ a$)=($i$,$ R$),\backslash$delta $($p$,$ b$)=($p$,$ L$),\backslash$delta $($f$,$ a$)=($p$,$ R$),$ and $\backslash$delta $($f$,$ b$)=($f$,$ r$).$

Then L$($M$)$ either accepts or rejects on every string beginning with b$.$