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, each represents a binary number that is divisible by
s
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, each represents a binary number that is divisible by
s
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);
charles.e.hughes@knights.ucf.edu
(e-mail is a good w
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Arup Guha
3/26/02
Example outlining the proof by contradiction that shows that the
Halting Problem is undecidable. In essence, I have written functions
that mirror the constructions of TMs given in the proof. What you
find is that no matte
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 reduced fraction (no common prime
factors) that equals
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 B, by definition of Union.
x A B, by assumption.
x B,
COT4210Spring2010Midterm#1Topics
1. Propertiesofsets,sequences,relationsandfunctions
a. Basicnotions
b. Prooftechniques
2. Computability,complexity,languages
a. Basicnotions
3. FinitestateautomataandRegularlanguages
a. Definitions:DeterministicandNonDeter
COT 4210
Fall 2009
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
a
b
b
b
ba
b
2.
Present the transition diagram or tabl
COT 4210
Fall 2009Sample Problems (Slightly longer than exam)
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 transition diagram or table for
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 of languages that can be recognized or accepted by
Det
COT 4210 Homework #6: Reducibility Solutions
1) Find a match in the following instance of the PCP:
Here is one solution:
.
.
In this arrangement, both the top and bottom read, ababababbaaaa.
2) Show that ATM is not mapping reducible to ETM.
Lets assume to
COT 4210
1.
Fall 2012
Sample Problems
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 -closures for each of As states.
State
-closure
b.)
A
cfw_A
B
cfw_B,C
COT 4210 Spring 2010 Final Exam Topics
1. Regular languages
a. Finite State Automata: Deterministic and Non-Deterministic
b. Right Linear Grammars
c. Regular Expressions
d. Regular Equations
e. Right invariant equivalence relations of finite index
f. Equi
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Arup Guha
3/26/02
Example illustrating paradox caused by Halting Problem.
Edited on 10/12/2010 to fit the format of Sipser.
public class TM_Sipser cfw_
/ H is supposed to return true if M halts on w, false otherwise.
public static boolean H(String
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Arup Guha
11/18/2010
Example of a polynomial time reduction from Vertex Cover to Subset Sum
Included is a 2^n solution for Subset Sum.
import java.util.*;
import java.io.*;
i
import java.math.*;
c
class subsum cfw_
private BigInteger[] numbers;
COT 4210 Quiz #2 (3/2/2012) Solutions
1) (20 pts 2 each) Categorize each of the following languages as either REGULAR (REG),
CONTEXT-FREE (CF), TURING DECIDABLE (TD) or TURING RECOGNIZABLE (TR). In
order to get credit, you must choose the most strict desi
COT 4210 Essay Rubric
Name: _
Category
Clear Thesis
Quality/Depth of Arguments
Concrete Examples
Consistency of Arguments
Research
Sub-Category
From UCF sources
From non-UCF sources
Communication
Clear Format
Clarity
Grammar
Writing Level
Total
Total Poin
COT 4210 Essay Prompt
Assigned: 3/13/2012
Due: 3/27/2012 (before class over WebCourses)
Maximum Word Limit: 1500
Please site sources as necessary.
Please turn in your response over WebCourses as a .doc, .docx, .rtf or OpenOffice document.
Question:
Inform
COT 4210 (Discrete Structures II) Exam #1 Solution
February 9, 2012
1) (15 pts) Let L, over the alphabet cfw_a,b,c, be described by the regular expression
.
Create a DFA that accepts the exact same set of strings described by this regular expression.
(Not
COT 4210: Discrete Structures II
Exam #2 Solutions
March 22, 2012
1) (15 pts) Let L be a language that is Turing Recognizable but NOT Turing Decidable. Prove
that it is impossible to create an enumerator E for L that enumerates L in lexicographical order.