1. Design Regular Expressions for the following languages. i. Strings that contains at least two 1's and exactly three O's. E={0, 1} Strings representing a word with length divisible by 4 and contains at least 1 vowel. E={a, b, c,..., z} ii. iii. Strings that contain '01' as substrings at any place except at the beginning or at the end. It accepts 1010,110110, etc. but does not accept 01, 0110, 1101, 00, etc. E={0, 1} iv. Length of the strings cannot be less than 3 characters and the number of 1's is divisible by 2. It accepts, 101, 1001, 1111, etc. however rejects e, 0, 1, 11, 100, 111, etc. E={0, 1} v. Strings where no character appears consecutively more than 3 times? E={a,b,c} Design DFA for the following languages. i. Strings that ends with 0 or ends with only one 0 after reading 1. E={0, 1} ii. The strings start with 'b' but do not end with 'baa'. E={a, b} iii. Each string contains 'abb' and has a length greater than 4. E={a, b} iv. Design a DFA for the language L where L={ 0'1 both i and j are odd }. For example, 01, 000111, 011111 are valid strings belonging to L. E-{0, 1} Convert the following Regular Expressions to their equivalent NFA/E-NFAS using Thompson's Construction. i. (0 + 10 )* 11 (0+ 0*1)* + (0+ 10)* (1+e) E=(0, 1} ii. (a*b+c)*(b+ e) E={a, b} iii. (a(b|c)*)*| (alb(a|c)*)* E={a, b} 2. 3.