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. Make sure you show the subsets in all nodes in the DF
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 differently.
n i = 1 + 2 + . + n
i=1
2 n i = 2(1 + 2 + . + n)
i=
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 a regular language
By denition, B is a regular languag
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 by Contradiction:
Assume A is a regular language. Then
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 Designer, http:/madebyevan.com/fsm/
2. (10 points) Exercis
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 = cfw_ai b j ck | i = j or j = k where i, j, k 0
The pu
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 free and the pumping lemma for CFL applies.
Therefore,