the alphabet for all questions below is assumed to be = {0, 1}.

This is to devise regular expressions, given an explicit definition of a language. For each languages, prove they are regular by giving a regular expression which describes them.

(a) L = {x | x begins with a 0 and ends with two 1s}.

(b) L = {x | x contains at least two 0s}.

(c) L = {1, 1111, }.

(d) L = {x | the length of x is at most 4}.

(e) L = {x | x doesnt contain the substring 001}.

(f) L = {x | |x| > 0, i.e. x is non-empty}.