Worksheet I: Alphabets, Strings, Languages, and Proofs
Date: August 27, 2013.
Problem 1. For each of the statements below indicate whether they are necessarily true, or not necessarily
true (i.e., fal
Quiz 5
1. Which of the following statements is true?
(A) There are languages that can be recognized by an NFA which cannot be recognized by a DFA.
(B) Languages recognized by NFAs cannot be recognized
Quiz 1
1. Let A = cfw_1, 2, 3 and B = cfw_, cfw_1, cfw_2, cfw_3, cfw_1, 2, 3. Which of the following statements is true?
(A) A B
(B) A B
(C) A B =
(D) A B = B
Correct answer is (B).
(A): A B since 1
Problem Set 4 Solutions
CS373 - Spring 2011 Due: Thursday April 7 at 2:00 PM in class (151 Everitt Lab)
Please follow the homework format guidelines posted on the class web page:
http:/www.cs.uiuc.edu
Solutions to Problem Set 3
CS 373: Theory of Computation
Problem 1. [Category: Design+Proof] For a string w , let wR denote the reverse of w, i.e., if
w = w1 w2 wn , where wi then wR = wn wn1 w1 . For
Problem Set 4
CS 373: Theory of Computation
Assigned: September 19, 2013
Due on: September 26, 2013
Instructions: This homework has 3 problems that can be solved in groups of size at most 3. Please fo
Solutions for Problem Set 1
CS 373: Theory of Computation
Assigned: August 30, 2012
Due on: September 6, 2012
Problem 1. [Category: Comprehension+Proof]
1. Let A = cfw_1, 2, 3, B = cfw_, cfw_1, cfw_2,
Midterm 1
CS 373: Theory of Computation
Date: Thursday, October 3, 2013.
Instructions:
This is a closed book exam. No notes, cheat sheets, textbook, or printed material allowed.
You have 90 minutes
Quiz 4
0, 1
q0
0, 1
1
q1
0
q2
0
q3
Figure 1: NFA N for problem 1
1. Consider the NFA N shown in Figure ?. Which of the following strings is not accepted by N ?
(A) 001
(B) 001100
(C) 10011001
(D) 1001
1
Equivalence of Finite Automata and Regular Expressions
Finite Automata Recognize Regular Languages
Theorem 1. L is a regular language i there is a regular expression R such that L(R) = L i
there is
Problem Set 1
CS 373: Theory of Computation
Assigned: August 30, 2012
Due on: September 6, 2012
Instructions: This homework has 3 problems that can be solved in groups of size at most 3. Please follow
Midterm 1
CS 373: Theory of Computation
Date: Thursday, October 4, 2012.
Instructions:
This is a closed book exam. No notes, cheat sheets, textbook, or printed material allowed.
You have 90 minutes
Quiz 10
1. In the notes for lecture 10 posted on the website, it is shown that the language L0n1n = cfw_0n 1n | n 0
is not regular. Consider the homomorphism h : cfw_a cfw_0, 1 dened as: h(a) = 01. Wh
Quiz 6
1. Let L cfw_0, 1 . Which of the following statements is necessarily true about L ?
(A) L is an innite set.
(B) L is a nite set.
(C) L is non-empty.
(D) None of the above.
Correct answer is (C)
Quiz 2
1. Let L = cfw_010, 101, 001, 011, and K = cfw_w | 0w L. Which of the following strings is a member of K?
(A) 0101
(B) 01
(C) 011
(D) 0110
The correct answer is (B). K is the set of strings for
Solutions to Problem Set 3
CS 373: Theory of Computation
Problem 1. [Category: Design+Proof] For a string w , let wR denote the reverse of w, i.e., if
w = w1 w2 wn , where wi then wR = wn wn1 w1 . For
Quiz 1
CS 373: Theory of Computation
Date: September 9, 2010.
Name
netid
Discussion
Tu 2-2:50
Lecture Section AL1.
Tu 3-3:50
Time limit: 15 minutes.
Tu 4-4:50
W 4-4:50
W 5-5:50
Pick the correct altern
1
Computing Using a Stack
Beyond Finite Memory: The Stack
So far we considered automata with nite memory
Today: automata with access to an innite stack
The stack can contain an unlimited number of
CS 373 Fall 2010
Quiz 6 Solutions
Lecture 1 Mahesh
1. C. For a grammar in Chomsky Normal Form, the number of steps in any derivation of a string w is
2|w| 1 (see problem 2.26 assigned as practice prob
Quiz 4
1. Which of the following statements is true?
(A) There are languages that can be recognized by an NFA which cannot be recognized by a DFA.
(B) Languages recognized by NFAs cannot be recognized
Quiz 1
1. Consider the set X dened inductively as follows: (1) (3, 5) X , (2) if (x, y ) X then (x + 2, y ) X ,
and (3) if (x, y ) X then (y, x) X . Which of the following pairs is a member of X ?
(A)
Problem Set 1
CS373 - Spring 2011
Due: Thursday Feb 10 at 2:00 PM in class (151 Everitt Lab)
Please follow the homework format guidelines posted on the class web page:
http:/www.cs.uiuc.edu/class/sp11
Quiz 11
1. Let be an equivalence relation and let E be an equivalence class of . Which of the following is the
strongest statement that is necessarily true about E?
(A) There are a, b E such that a b.
Midterm 2
CS 373: Theory of Computation
Date: Thursday, November 4, 2010.
Instructions:
This is a closed book exam. No notes, cheat sheets, textbook, or printed material allowed.
You have 120 minute
Quiz 12
1. Consider the grammar G = (V = cfw_S, A, C, X, Y , = cfw_a, b, c, R, S) where the set of rules R is as
follows:
S AX|Y C
A aA|
C cC|
X bXc|
Y aY b|
Which of the following strings can be deri
Problem Set 2
CS 373: Theory of Computation
Problem 1. [Category: Design+Proof] Let Ak cfw_a, b be the collection of strings w where there is a
position i in w such that the symbol at position i (in w
Solutions for Problem Set 6
CS 373: Theory of Computation
Assigned: October 18, 2012
Due on: October 25, 2012
Problem 1. [Category: Comprehension] Consider the PDA P over the input alphabet cfw_0, 1,
1
Undecidability
Undecidability
Denition 1. A language L is undecidable if L is not decidable. Thus, there is no Turing machine
M that halts on every input and L(M ) = L.
This means that either L is