Algorithms-1 HW

Transcript

1. problem1 Streng n alphabetT S N 2T T thesetofstringsont l n EIN Concatenation of strings Let Txt T R l d on x r 27 if 1131 1 I Ll m a B Mtl 7T a p i acid it in pco et i m R 37 it 13 22 x 1B a.pl p't n n11 Reverse of astrong LE Let hr 0 121 0 a X TR p ar 12120 212 yr CHR Length of a String s Domain Concatenatingpowerof strings anam an m Associativity of concatenation L B y L pig Language on an Alphabet is a Language on T 1ft LET't
2. problem2 Cexp ReeCi aoa Cexp Ree ca anti Canta etneo 1a1 120 1111 0 0 Ial p i let nik I H 121124 Hal Letn k11 24 12 t 2K at 1471114 IH kKall Ck 111121 problems F R 2 let 121 0 d X Mr f R R HR p RI Rt let 121 n I H 2942 let 121 Intl LMR R z d Cal k R calm k Cj r I H CLE Cyr R je I e R one car x e ar y
3. problem4 Ln.am D Can ar i x am anim m O a 3 d go L X y m k k I H a a yr1K m K11 Ln yet R3 an k.yyAEsocfyn.jkJ2 f2ntkJ.p ExpRec 2 dntk11 yntm 2 Can R ar n O go R A R X ar Car d I H Can k ar n t1 ecs H R Cx 2 R 2K Ca'T exoRec a LR e k I H part µpytk Mr
4. Problems i WE prove w.wrjr w.br w.wR7R w WR cec's 2 Tae CLE REL co.ir cz.io73 pr0bkmL ggyciy gLci ificlalBci laDiflLlEiclxl 1131 IPF INE ie Kl 11 i Ea Bci 1217 136121121 p co p e I H L g Ci La E clal Bci Iai ifldleic IN11131 Btn 11 121 Eic 1211431 Es k e pry Ka.pl 84 112pe 11 R L Lin 11 1211181
5. problem 7 provethat foranytwostrings 413E C dope Ca.pje peso PEEpe a EcaseBIO ish a jdp.ycc2peprje ca.jsej.prfca.pe pt I ka.pej.prjciy gx.pe i 42pe k2 pe prcip1ea.peIjfg4i l2P4 CcapeIpr ci7f1C peHPrt 11 fc2 pe prkijflct.pe 11 11 d pr problems L p r Pr B12 2 B k pl 1 p YI Cap 121 1 7T is idol k Bhi Cape prr plot i lm cct.pe.pkG.pejpT i Ccx.peJ prJC x petiprl n Cpf2peJ.prX1a.pe1
6. problem9 BY problem2 HnEIN F la I nIal la1 1 Tn cIN Idnt n n 272 ET St 121 4 problem 10 44 0 w IWRl 14 1 1 0 1w I H Iwl n lwRkn w ntl Iwm wr.cat wrlt fwe4 1wrltn n t I
7. Problem11 Let T a am bean alphabet and Let pi denote the i th primenumber i e poiZ p 3 pz s etc Let G T IN be thefollowingfunction Ella O 9in ToPair11 Forinstance GCcase go7 263 provethat G is 1 1 BY Uniqueness of Primefactorization GChaco au D TT K o P I G Lag ao27 zs 301 26.31 byfundamentaltheorem Pco z put3 ofarithmetic G e IN D 7 1