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ALGO_FA09_T1 - (15(15{20(l5(20(15 MAQ 3512 TflEQRY OF...

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Unformatted text preview: (15) (15) {20) (l5) (20) (15) MAQ 3512 - TflEQRY OF ALGORLTHMg FLORI ‘ NT'L IV. T§§T fll - EfiLL '09 ' . TIME: 75 min. Answer' all 6 questions. Provide all reasoning‘ and show' all working. An unjustified answer will receive little or no credit. BEGIN EACH QUESTION ON'A SEPARATE PAGE. 1. (a) Define what is a regulaz'expression over the alphabet {0,1,2}. (b) Convert the NFA on the right into an equivalent DFA. Find regular expressions which describe the languages below. (a) L1 = {a€{a,b}*: G contains both be & abb as substrings} (b) L2 = {Be{a,b}': 6 has at most two occurrences of ab} (a) Find all the inaccessible states in the DFA below. (h) Then partition the remaining states into blocks of indistinguishable states and find the reduced machine. ...-."-.—.._..~..._n.__.._—..-........._—_u_...._—......_-_......._—....n..- Find a DEA which accepts precisely the strings in the language L4: {0)E{a,b}*: f(m)>1}, where f(m} = [2nh(e)—na(w)-3](mod 4), and then check your DFA with aaba as input. e-mfii 1» .Sfilk - .M . .r - _. fi“' r J (a) Define what is an inherently ambiguous context free . language. (b) Find a context—free grammar which generates the language L5 = {afif: k>3n} a {bRflQ: k<29jl}. \- \ re. «pg. Let A, B, and D be languages based on the alphabet {a,b}. (a) Is it always true that (A.DC)U(B.DC) c (AuB).DC ? (b) Is it always true that (A-B).D t (A D)-(B.D} ? Justify your answers completely. MA’D 5572 " 77M”): 0/ fl/Zér/flmx Fla/7‘42 57/ 7 1/17/34 Sa/bzfmn: 7’5- Zest-gt 1 Fa?” 22.519. rm) fl rye/Jaw m/preswbn war {27,42} .15" aééze/ weary/ye? “as 6/5143, (l) 3,9,! 2 grid Q5 are rgaér ax raw/MI, "I... 1/!) // E &F are 9137, M/fi'} 2721:?” $9 are (Sf-£2 Efjéi (5*) .. . . — a £25 5”)- ° {5,5} (I: j/fifim} .,7 7 A; i .. RQ) : {A}< ¢ a??? { 5 C31\>-FA,8}C} Tan-,4 is {A3 ° (@[email protected] 52(4)::~-~5a....a$é~~ -..4M..-Ja»- m. Mama/”55155.“; I 2 75, = (4+..éf- (gee. (MW? r- fééetéfée + 9.444 «flaw/T (A): Ma 4/: G 2 m at; ”4/ m 4%} My / if 96- 1‘96 .52. 3 éféf’ 7"” £49545. [2* 7" 5221:4741???" 455? 3(4) ' / 0 Dx .7 a} A /- 0 [3" "CP‘ um} 23/ flex“ B/G/O/Eqfia - 1’» F drfid’ H are [mattress/454? Sigzéf (bi/3: {mm} {ca—:4} _ .3: mm; 5.6) €55? fl: 279,03 {83 563 22-35) *@ .3 {M} £63 m rem; - I; (WAS {33 5c} {53 I43 - @ 4(a) :Zet A.) (Jr—g),/,2,3) 5:: de Sié'lé mi 3/27)?“ 726 Mgr/”47%” ftmz‘ #5)») a { (W14). #0) —.= [email protected](A)~»4{A)~3 1:435} {mum/4)) 5’)? fl.) wgfl 53 fig /3?)“/xfl/ 32%))? x41“? 1‘}; 4/115 sz/ ée fly, away/n7 57%)?) 3mg) -/@)>.Z gm,“ 7%»: 2 w sigma/41' Hwy/7 ' 4/5):an = zzaééuaJWaW) «3 = 2%»st ~/ =-~ Aw»)??? f9?” = 2275 GM) wfiawé) *5 = 245(0)) ‘34)?)“3 +2 7-)???)7‘2 (“f/{9 (j) /M/) ”2L: - a a: 6‘ d Ska/es: F7; ’40 A3 A! ’40 Mei: {@1254} r; 2(/_) ~523- = ~4— 3 0 M0/@/ 5742/4)? ffiérfl’d’fliyy flméf mu“ (Fl Ar 4 Kmyage 14/; [5% .3650? éejfnérafé/ 5 a (756 544/ Canna/ A2 feflyraZéy/ . $5} an unaméiyum): (F6. (6), S") ’4/‘3 ju/eJ 7X5 tin/o)? ' A —-> aaa/M/aA/é. . idle: {awflfl‘ofifix né-‘g/ao] { B «a mac/cc} pa 6/) 69m; mfg“, kswn} 45:9}! «w» aB/‘M =9 dé/jéar—i % dw/Uflsa r-w-«baméfé’fl4ziglw/2’? .is a» 8 => me a; mag...) r; flax ._.., flu“? we"? 5W5VES. ZeZz {/26 (Aflfiuésfic). mwwwzz)‘ a», fie 50C ”:23? Me 744/ (are ¢= my an}? yoga/#4 X62): Jo [email protected]&4u/b’).x)c, 4744/ 1/7 721cc: fézpn6 {an [3,5 wr/Z .. figfi wn/ £541); 50 ¢e (Ah/8372): gig-3);). .30 m" m/Z’ax ”(are y C.- mmw‘? .: 04.2“? 0,133.3“) g (Au/3).)OC (AM). [at/- A =‘ {a}; 5445; and a z 52,5}. .742): “14'3"- 3,2, = {533.316} ~ {d5},§1,b] :: €42,416} - [aéfiééf =44} ..MJ(A—3).D =({4}-Wj).{x],b} .- m}.m,)}= {4,515} ,_ so ilaé .5 (2+5)? m‘ cm)! M-w . 4W...) (A-E),,0¢§4,p)_{3,b)_ ...
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