CSci 423 Homework 2
Due: 9:30 am, Thursday, 9/17
Stephen Yuan
1. (10 points) Exercise 1.7 (c) on page 84 and then additionally convert the NFA to an equivalent DFA
using the subset construction method
CSci 423 Homework 1
Due: 9:30 am, Thursday, 9/10
Stephen Yuan
1. (10 points) Prove by induction that n i3 = (n i)2 .
i=1
i=1
Proof: To start, we will represent the right side of the equation different
CSci 423 Homework 5
Due: 9:30 am, Thursday, 10/15
Stephen Yuan
1. (10 points) Problem 1.49 (a) and (b) on page 90.
(a) Let B = cfw_1k y|y cfw_0, 1 and y contains at least k 1s, for k 1.
Show that B is
CSci 423 Homework 4
Due: 9:30 am, Thursday, 10/15
Stephen Yuan
1. (8 points) Prove by the pumping lemma that the language A of strings of 0s and 1s whose length is a
power of two is not regular.
Proof
CSci 423 Homework 3
Due: 9:30 am, Thursday, 9/24
Stephen Yuan
1. (10 points) Exercise 1.12 on page 85.
DFA:
a
b
a
a
b
b
b
a
a, b
Regular Expression: b(bb)*(aa)*
Collaborators: Finite State Machine Des
CSci 423 Homework 6
Due: 9:30 am, Thursday, 10/22
Stephen Yuan
1. (6 points) Give an informal description of a pushdown automaton that recognizes the language
A. Give the state diagram of your PDA.
A
CSci 423 Homework 7
Due: 9:30 am, Thursday, 10/29
Stephen Yuan
1. (20 points) Problem 2.30 (a) and (d) on page 157 (131).
(a) L = cfw_0n 1n 0n 1n |n 0
Proof by contradiction:
Assume that L is context