Can you help me with the following exercise? 1. legible handwriting please EXERCISE TO SOLVE:

2. I have attached a similar exercise of how I would like the exercise to be solved a)

b)

c)

DESING A DETERMENTST FENETE AUTOMATON THAT ACCEOTS THE LANGUAGE CF BENART STRENGS WITH av Even NUMBER OF I's: a) Descrebe it formally b) DRAW the transIIION diagraM and THE State table C) DEMOSTRATE THAI THE AUTOMATON INDEE. ACCEPTS THE LANGUAGE OF STRTNGS WITH AN EUEU NUMBER OF I. IMPORTANT INFORMATION: EXAMPLE a) Descrebe it formacli CONSTDER THE AUTOMATON A=(Q,,8,90,F) DFFINIDE AS 1={0,1},Q={90,q1,q2},F={q2} AND TEE TRGU SIILONS GIUEN BY: \begin{tabular}{lc|cc} (q0,0)={q0,q1} & & 0 & 1 \\ (q0,1)={q1} & q0 & {q0,q1} & {q0} \\ (q1,1)={q2} & q1 & & {q2} \\ & q2 & & \end{tabular} CS Escaneado con CamScanne TRANSITLON DLAGRAM: II IS A DIRECTED GRAPH 6=(U,E) DEFINIDED AS: 1. EACh sTATE qEQ is asJoctated to a NOdE rEE 2. FOR a,p EQ and a E III(a,a)=P THeU THERE IS A TRANSITIOU CP,q E E' FROM IHE NODE ASSOCLATED WITH 9 TO THAT ASSOCIATED WIHH P. 3. THE INICTAL NODE qO has an arrow WITH NC PRECEDLNG NODES. 4. THE TERMINAL NODES QEF arE marked WIIHA STATE TABCE: REPRESENTS THE FUNCTION In TABULAO Form T AS: 1. THE ROWS ARE ASSOCEATED TO DE STATES GEQ 2. IHE COCOMNS REPRESENT THE SYMBOCS aE 3. The intilac state is manked with and THE FINAL StATE WIIHA. 4. EACH ENIRY IN THE TABLE IS CF IHE FORM: C) denostrate thar... tiE AUTOMAION DEfEntDED aboUE DEFEnES THE LANGUAGE: L=[[(0,1)01]] TO PROUE THES, IT MUST BE SHOWU THAT: 1. q1^(q0,w) if and only if w cnos in O 2. q2^(q0,w) If and only if w ends in OI DE mOSTRATEOU FOR 1 SUPpOSE q1E^(q0,w) If w=1 THEN w=x.q but aurzaraar since 91 is passed ontr with 0 , iHen a=0 and arta w=x.0. Sufpose w ENDS EN O. IF W=1. THEN w=0 AND THEREFORE (q010)={qq1q1}. AND THCMEFORE q1 ^(q0,0) If T>1 tHEN =xC AnD Hence ^(q0,x0)= {90}{q1}={q0,q1} DTMOSTRATEON FOR 2 SOPPOSSE q2E^(q0,w) THEN w2 If w=2 THEN W=O1. SENCE TO REACH QZ THESE STMBOCS HAUE TOBE CONSUMED. IF W>2. THEN W=X.01 SENCE WE CAN ONLY 60 TO 92 bY CONSUMING O and 1 . SOPPOSE W=x.01 ENDS INO. DECOMPOSE INTO W=y.1, y=2.0. BUT Y ENDS INO,AND BY THE PREULOUS EXTENSION ^(q0,y1)=Ui=1n(0,1) wiTH fi (q0,y) FROM HERE WE HIUE tHat qzo (q1,1)&(q0,y.1) From thes it is obtatnes that the lancuage of the AutOMATCN is L=[[(0,1)01]]