ConsidermodelingtheproblemofafarmerthathastotransportaGoat,aWolfandCabbage inaboatacrosstheriver. Initially$($startstate$),$ thefarmer isonthe leftbankof theriver. Furthermore,theboatcancarrythefarmerandonlyoneoftheotherthree.Thefarmerand hisentireentouragehas tocross totherightbankof theriver. Notethat the farmercan $1$ferryeachofthethreebutoneatatime.However, ifthefarmerleavesthegoatandthewolf unattendedoneithersideoftheriver,thewolfwilleatthegoat. Ifthefarmerleavesthegoat andthecabbageunattendedoneithersideof theriver, thegoatwilleatthecabbage.Your taskistomodel thisproblemasaDFAandthendetermineasafesetof$$moves$$thatwill transportall fouracrosstheriver.A$$safe$$stateisonewheretheitemsonthesamesideof theriveraresafefrombeingeatenbyanotheritem$($i$.$e$,$cabbageisnoteatenbythegoatand thegoatisnoteatenbythewolf$).$A$$move$,$anda$$move$$isatransitionlabeledbyeither F$,$G$,$C$,$WwhereFdenotesthe farmeralonecrossestheriver,Gdenotesthatthe farmer andgoatcrosstheriver,Wdenotesthatthefarmerandwolfcrosstheriver,andCdenotes farmerandcabbagecrosstheriver. Belowaresomehintstogetyoustartedwithmodeling thisproblemusingaDFA: $$ thestartstatehasall fouronleftbankof theriverandnone$($emptyset$)$ontheright bankoftheriver. $$ eachtransitionwill endupchangingthecontentsonthe leftbankandrightbank$($for example,atransitionlabelledCfromstartstatewill leadtoastatethatdenotesWolf andGoatonleftbankandFarmerandCabbageontherightbank$).$Notethatthefarmercancrosstheriveralone $$Thefarmercancrossfromlefttorightbankorfromrighttoleftbank$($withorwithout otheritems$).$Thefinalstate$,$ thatdenotesasafetransportationofall theitems,willhaveall fouron therightbankoftheriver.