Sample Assignment # 3.1
Present a transition diagram for a DFA that recognizes the
set of binary strings that starts with a 1 and, when
interpreted as entering the DFA most to least significant
digit,
Sample Assignment # 3.1
Present a transition diagram for a DFA that recognizes the
set of binary strings that starts with a 1 and, when
interpreted as entering the DFA most to least significant
digit,
Discrete II
Theory of Computation
Charles E. Hughes
COT 4210 Fall 2016
Notes
Who, What, Where and When
Instructor: Charles Hughes;
Harris Engineering 247C; 823-2762
(phone is not a good way to get me
COT 4210
Fall 2014
Sample Problems with Solutions
1.
Let L be defined as the language accepted by the finite state automaton A:
a.)
Fill in the following table, showing the -closures for each of As st
Key Assignment # 3.1
Present a transition diagram for a NFA that recognizes the
set of binary strings that starts with a 1 and, when
interpreted as entering the NFA most to least significant
digit, ea
Assignment # 2.1 Key
Let L be a language over cfw_a,b where every string is of even length and is of the
form WX, where |W|=|X| but WX. Design and present an algorithm that
recognized strings in L usi
Assignment # 1.1 Key
1. Prove or disprove that, for sets A and B,
A=B if and only if (A ~ B) (A B) = A
Part 1) Prove if A = B, then (A~B)(AB)=A
Assume A=B then (A~B)(AB)= (A~A)(AA)
Now, any set inters
Sample Assignment # 4.1
Convert the following NFA to a regular expression, first by
using either the GNFA (or state ripping) or Rij(k) approach,
and then by using regular equations. You must show all
Sample Assignment # 1.1
1. Prove that, for sets A and B,
A=B if and only if (A~B)(~AB)= ,
where ~S is the complement of S
Part 1) Prove if A = B, then (A~B)(~AB)=
Assume A=B then (A~B)(~AB)= (A~A)(~AA
Sample Assignment # 2.2
(I have no sample for 2.1)
Present a language L over = cfw_a where L3 = L4 but L L2 and L2 L3
Note: Lk = cfw_ x1x2xk | x1,x2,xk L
Proof:
Consider L = cfw_a* - cfw_aa, aaa
L2 =
Sample Assignment # 2.2
(I have no sample for 2.1)
Present a language L over = cfw_a where L3 = L4 but L L2 and L2 L3
Note: Lk = cfw_ x1x2xk | x1,x2,xk L
Proof:
Consider L = cfw_a* - cfw_aa, aaa
L2 =
COT 4210
Fall 2014
Sample Problems Key
1. Draw a DFA to recognize the set of strings over cfw_a,b*that contain the same number of occurrences
of the substring ab as of the substring ba.
b
a
a
b
a
ab
a
COT 4210
1.
Fall 2014
Sample Problems with Solutions
Let L be defined as the language accepted by the finite state automaton A:
0
A:
0
1
B
A
1
D
C
1
E
0,1
a.)
Fill in the following table, showing the
Sample Assignment # 5.1
For each of the following, prove it is not regular by using
the Pumping Lemma or Myhill-Nerode. You must do one
of these using the Pumping Lemma and one using
Myhill-Nerode.
a.
COT 4210: Discrete Structures II
Exam #1
September 23, 2010
Name: _
Lecturer: Arup Guha
(Directions: Please justify your answer to each question. No answer, even if it is correct, will
be given full c
COT 4210: Discrete Structures II
Exam #1
February 7, 2013
Name: _
Lecturer: Arup Guha
(Directions: Please justify your answer to each question. No answer, even if it is correct, will be
given full cre
Spring 2015 COT 4210 Exam #1
February 19, 2015
Name: _
1) (10 pts) Design a DFA that accepts the following language over the alphabet cfw_a, b: L = cfw_ w |
w has exactly one occurrence of the substri
Synthetic Reality
Lab
University of Central Florida
Co-Directors: Charlie Hughes, Greg Welch
Avatar mediated interaction
Microposes
Manifestations of surrogates
Applications to teacher practice, train
Fall 2014
HUGHES
SYLLABUS
Dr. Charles E. Hughes
Office: HEC247C; [email protected]; Use Subject COT4210
Class:
TR 1:30pm 2:45pm in MSB-359
Office Hours: TR 3:15pm 4:30pm
GTA hours:
Mela
COT 4210
Finite State Automata
D.A. Workman
Finite State Automata
Our next series of definitions and results characterize the family of Regular Languages.
Specifically, this family is exactly the set
COT 4210
Finite State Automata
D.A. Workman
Finite State Automata
Our next series of definitions and results characterize the family of Regular Languages.
Specifically, this family is exactly the set
Fall 2014
COT 4210
HUGHES
SYLLABUS
Dr. Charles E. Hughes
Office: HEC247C; [email protected]; Use Subject COT4210
Class:
TR 1:30pm 2:45pm in MSB-359
Office Hours: TR 3:15pm 4:30pm
GTA ho
Sample Assignment # 1.1
1.
Prove that, for sets A and B,
A=B if and only if (A~B)(~AB)= ,
where ~S is the complement of S
Part 1) Prove if A = B, then (A~B)(~AB)=
Assume A=B then (A~B)(~AB)= (A~A)(~AA
COT 4210
Fall 2014
Sample Problems Key
1. Draw a DFA to recognize the set of strings over cfw_a,b*that contain the same number of occurrences
of the substring ab as of the substring ba.
2.
Present the
COT 4210 Fall 2014 Midterm#1 Topics
1. Properties of sets, sequences, relations and functions
a. Basic notions
b. Proof techniques
2. Computability, complexity, languages
a. Basic notions
3. Finite st
COT 4210
Finite State Automata
D.A. Workman
Finite State Automata
Our next series of definitions and results characterize the family of Regular Languages.
Specifically, this family is exactly the set
Assignment # 2.1
1.
Prove, if p and q are distinct prime numbers, then (p/q) is
irrational. Hint: Look at next page.
Assume (p/q) is a rational number where p and q are distinct
primes. Let a/b be the
Sample Assignment # 1.1
1. Prove or present a counterexample to the statement that, for nonempty sets A and B, AUB=AB if and only if A=B.
Part 1) Prove if AUB=AB then A=B:
Assume AUB=AB.
Let x A
x A U
5
COT 4210 Spring 2017 Midterm#l Name: K E
Total Points Available _7_5 Your Raw Score X
Gradu
1. Present the transition diagram for a DFA that accepts the set of binary strings that represent
numbers
COT 4210 Fall 2016 Midterm#1 Name: Z EY
Total Points Available Q Your Raw Score Grade:
4 1. Present the transition diagram for a DFA that accepts the set of binary strings that represent
numbers tha
Generally useful information.
The notation z = <x,y> denotes the pairing function with inverses x = <z>1 and y = <z>2.
The minimization notation y [P(,y)] means the least y (starting at 0) such that P