Question

1. (15) Let L be the language over {a,b,c} accepting all strings so that: 1. No b's occur before the first c. 2. No a's occur after the first c. 3. The last symbol of the string is b. 4. Each b that is not the last symbol is immediately followed by at least two c's. Choose any constructive method you wish, and demonstrate that is regular. You do not need an inductive proof, but you should explain how your construction accounts for each rule.

Answer 1

sol":- Given L be the language over {a,b,c} accepting all strings so that : 17 No b's occur before the first c Then lean since } Then we take cb* (c, cb, ebb, --3 = { 1, b, bb, 2) No a's occus after the first c. can take ak e {c, ac, aac, a.ro -3 37 The last syntol of thes the string is b Then combiniting above three strings we get regular ac bb* that is not the last symbol is immediately followed by at least two c's Then the c} the ex pression 47 Each b accepting Larguage Lones ha,6,

2 3 ③ and 9 is given all strings given in by ах (and) Ле Herce L= atc cac bbh 0, C c*c bb* Since that s, a, b, c expressions and the union, contafenation of two reguar expressions is also a regular expression is a regular expression. primitive regular closure Ans)