Try to design a context-free grammar for each of the following
languages (it is not always possible). Whenever possible, make it a regular grammar.
a. The set of all strings of 0's and 1's where every 0 is immediately followed by at least
one 1.
b. Strings of 0's and 1's with an equal number of 0's and 1's.
c. Strings of 0's and 1's with an unequal number of 0's and 1's.
d. Strings of 0's and 1's that do not contain the substring 011.
e. Strings of 0's and 1's of the form xy where x and y are equal-length strings and x 6= y.
f. Strings of 0's and 1's of the form xx