Given the language L$=($a $|$ b$)*$ ba$*$a over the alphabet $\{$ a$,$ b $\}$ :

Construct the DFSM that accepts L$.$ If you wrote a NFSM$,$ then convert it to a DFSM$.$ You may either draw the DFSM or describe it formally, but the states Q$,$ the start state q$0,$ the accepting states F$,$ and the transition function $\backslash$delta must be clearly specified. $[6$ points$]$ L$=($a $|$ b$)*$ ba$*$a