CS 162  Automata Theory Homework 4, 25 Points
Due: Friday, February 10, 11:55pm

5 points.
Let L={0^{n}1^{2n}  n > 0}.
Give a CFG for L.

5 points.
Show that every regular language, L, is also context free.
Hint: use a proof by induction on the number of operators
in a regular expression for L.

5 points.
Exercise 2.5(b,c,e) in Sipser.

5 points.
Exercise 2.14 in Sipser.

5 points.
Let L be the language of all strings, w, of 0's and 1's such
that w has an equal number of 0's and 1's (in any order).
Give a PDA for L.
Include comments in your answer describing your PDA in English as well
as using a transition function.