# Homework Assignment #1

#### Due on paper in class, Monday 7 February 2010

There are twelve questions for 100 total points. All but one are the textbook, Introduction to the Theory of Computation by Michael Sipser (second edition). The number in parentheses following each problem is its individual point value.

• Exercise 0.5 (5) Prove your answer by induction on the size of C. That is, for your answer function f(n), prove "for any non-negative integer n, for any set C of size n, the power set of C has f(n) elements" by induction on n.

• Problem 0.12 (5)

• Exercise 1.3 (5)

• Problem A-1 (10) Find a regular expression for the language L(M) of Exercise 1.3.

• Exercise 1.4 parts a and g only (10)

• Exercise 1.6 parts d, i, k, and l only (10)

• Exercise 1.10 (5)

• Exercise 1.17 (5)

• Exercise 1.28 (5)

• Problem 1.38 (10) You should prove that any language is regular if and only if it is the language of some all-NFA. One direction of this is very easy.

• Problem 1.45 (10)

• Problem 1.48 (10)

• Problem 1.49 part a only (10)