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ALGO_SP09_T1 - MAD 3512 THEQRZ QE ALGORITHMS ELORIDA INT'L...

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Unformatted text preview: MAD 3512 - THEQRZ QE ALGORITHMS ELORIDA INT'L UNIV. TEST El-EPRHVG“Q9 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. (15) l. (a) Define what is the extended transi- tion function of an NFA. (b) Convert the NFA on the right into an equivalent DFA. (15) 2. Find regular expressions which describe the languages below (a) L1 = {ae{0 1} a contains both 01 e 100 as substrings} (b) L2 = {BE{O l} B has at most two occurrences of 10} (20) 3. (a) Find all the inaccessible states in the DEA below. (b) Then partition the remaining states into blocks of indistinguishable states and find the reduced machine. (15) 4. Find a DFA which accepts precisely the strings in the language L4 = {u)€{a, b} [2n (m)- 3nb(m) 1] (mod 4) < 2} and then check your DFA with aaba as input. (20) 5. (a) Define what are inaccessible productions and noc- terminating productions in a CFG G. (b) Find a context- free grammar which generates the language L5 = {ckbn : k>2n} o {bka " : k<2n+3}. (15) 6. Let A B and C be languages based on the alphabet (0,1). (a) Is it always true that (A. C )o(B. C ) ; (At -B) C ? (b) Is it always true that A.(B-—C) c; (A. B) (A. C) ? Justify your answers completely. - iii/744D 3-672~ 77760:" of 24/ or/flms F/or/a/d /n2‘€rmf/W7a/ “WV— % WW iiéSo/a/Ibns 73 79332[ 549 / _ S‘Zw'fZ 361‘}: Hi 1T: . . .- . “whine Px/enfl/ fram‘x/fon flgfigfibfl Ax: 62x21“; 5%» 0/ an ”/54 2'} A“ . , . jgi/S 13/051571 j} A (/0! 4)) :1: fig 62 ‘r 51'} Cd}? éfi/j/(Ju £pam./p AL 3} 3!? 0 {51* (5);”; ° 73 ’6'" i1? ”’9’, \J\ A 3:520).- {my , { arm it; T*"4Ansh { ' iii -. 0 W éai ”W = 0 3:?” @fl 1:; i ii; .. 2 @0315; ~ - - - 0/ - — $100 J loomw-w) - - — 0m: --J mm @551 = ’(Q+1)*('_01.(9+1)"7!_09 + 199.69% 91 + 52105? + lagwf ;ii ' :1; , , (5);: No l0! 2 me /6 2 fave: A9: {@352 " ff" Pf! 1" .0? + .0579 flit/chi” E 0’? 37"}: f“. 3 (60%;; a A ,2» F a 3; F “T9“ c; x1 ‘79“ 3 D afld’ 2‘7 are zfidtes's‘fé/g s/afes (93335: {A 6; F], {6,5, 4‘} P; {A,5,F}) {'ch {5,4} ‘fz MFUBL {cg’ {5, a} -«——>—{A,F} £13: MP}, :31, e‘cm‘ews r12 {/41 F}, m, {cues , w} P3 . 3. 4(a) Zef fcw) = fifiatw3"3”¢(WJ--l (wag/9'6) gm] M A" ([3: anag) 6’78 1%? .S/Lafe flmf 55/5314; fie Mfirmaz/rafi #4? flags-E (Wad/é“) 4(a):§7Zzen 1(0) = ZXQQJ— 5/2;(/U-/ = that-l 5 36247014), 5'0 A3 Mi 1:3 Ac: fie awféa/ 3/41/19 - oar/24’ ,4, “”7/ jg 7%,:- ac'é'g/DZI/fljj- 372$; éerease e < 2 mm/ /<'.2 #190 El EL: 7%“) = 2/7491“).- 5’wad)~ / = 2’7e(w)—3fib(w)“/ 1‘2 £ng 72/7720”) f‘Z/db) 3 2”a(“5) — 3195(wé)~/ 1 2/2400- 3/35/41!) "I -- 3 :5 Hadfl (ma/41) 51—)..____.(___AI1 ([2) whcd: a it 5 a” a g )4 swag: [/13 ,4, A3 ,40 42 a 6’65!) fl” wetness/We (W cm reecAaX/e)/ora/ac/mn /5 one wémé Moro/Vex a ehecé :' .2 ”Mada/761w) —/= 2(3)~3.-/ & 2mm Var/215k; fiafi egg/mall fie reg/Ae/ 740m #8 mgr/”y L/erneé/e 53:4 7’10"! féfm/ndljiky ;/o/ucz5en rs awe. fiat ram/ye: e: Var/£254: féef g‘e’oe: mf fermma/e er [read if: 5ame7/2/hj' 7%ef erm/aafl fermzhaz‘e; ‘ (5);: S --> 14/5 gill/ES 72.9 art/Faun i: A —=> cc A A / eA/(f gen/Brodie: {czflfl‘ffiflr 77353701213} B '4' DDEa / 32)) 35> 5/) genera/”e: - {5“ a” _' (J sksmwj , anp E . - BAH/,7 S a? ’4 "5‘ C2345 ‘=}’ CqAézza-a =3: 670/46” =9 canc/Hflzza-ué c ” Afr/c x 5:35 ==> D2512 :91)?qu =3: :9 “OWE/I” =5 Dubber" = Dzmaflaé an , ossqum‘z. M4)”: V55. [ell 9'95 (24.6) 1/ (6,67%), 72m gig A-C‘*er gee BL} ”:50 4; = oz, X, for same oc’e‘ A meal EGG"): err 90 1 Some fie 5 am/ 3956*. In fie Arrz‘ and ()1 ::. o(. X, aux/2’ are (Au/3) em/ X 6 (j i 5‘0 {06 (HUB) 6* 414/ m 7% segona’ (eye ‘11:? F XL 2 aux/Z 13:04:16) am/ 3366 5‘5) gee X4915) 5 So an e/flfl ,:3. We; (Au/3). C_ Ate/nee (AC )0(8.C *1) £3 (fulfilC H 7“- NR 3* (nflé/VU. Leaf A = {0,01% 2 3 '-‘ {1}, 41/71 6.:f/1], 74.222 54; = {1}. So INK-c) 7; {0, 01}. {1} = {0/ on} ,4 3 = M or? {1}: {0/ 0n} .— f0,0l].fll}: {or/om} mm’f {-A 5} (A. c)-— {0/ art] {on 01/4;me .; Hence. /-1.(B~C) : {a}, 01/} ¢ {01‘} z (A g)- (A C.) Em: ...
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