Question

please tell me how to do (p), (s), (t).

85 Exercises EXERCISE 1 on for each of the following languages. Give a regular expression for each of the follow ke the machine from 0 back, a. label rip from 0 back co state 0 on an input b. {abc, xyz] c. a, b, d. {ax | x € {a,b]"} e axb | x € {a,b}} [ {(ab)"} assing through 0. bo a piece we already have a input string. So the whole state 0 back to state 0 any mmmm FA—the language of strings ree. expression for the le just shown, defining the paths through the NFA. those details, let's put all b* x contains at least three consecutive as by the substring bab occurs somewhere in x slable x starts with at least three consecutive as b}* x ends with at least three consecutive as) k fx € {a, b}* | * contains at least three as} I fx € {0, 1}* x ends in either 0001 or 1000} XE (0,1}* x either starts with 000 or ends with 000, or both} n. {d"In is even} {b" nis odd} 0. {(ab)"} {(aba)"} p. 1x € {a}* | the number of as in x is odd} 4. fx € {a,b} * | the number of as in x is odd} Ixela, 6* the number of as in x is odd} { bnis odd} {(aba)" ${d" | n is divisible by at least one of the numbers 2, 3, or 5} t. {x {a, b}* | x has no two consecutive as} u. {xy e {a, b} * the number of as in x is odd and the number of bs in y is even} EXERCISE 2 ir tuo NFAs the exact one constructed by the monly if it is L(r)

Answer 1

(P){xchaft / no. of as in x iz odd} 2. Sa, aaa, aaaaa, - - - - } &- alaalt (S fan, Inis divisible by atleast one of numbers 2,3,& s} { ¢, ah, a, a, ah, _ .~ } >©9@?@ 1890 (reef (aas + Canal + coranas)

60 freda, bet no two coneccutive a's} The regular expression for this can be written as: ore ( 6* (67ab)*** +a) So, which generales only a follorea By but not a followed by a 3 is reject state