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World Citizenship Competition
2015 Season
Version 1.0 September 10 2014
OVERVIEW
The Imagine Cup World Citizenship Competition honors the most innovative, impactful, and l
ProgrammingLanguages
Syllogisms and Proof by Contradiction
Midterm Review
Dr. Philip Cannata
1
Notions of Truth
Propositions:
Statements that can be either True or False
Truth:
Are there well formed
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Cover Automata for Finite Languages
Michal Cadilhac
Technical Report no 0504, June 2005
revision 681
Abstract. Although regular languages combined with nite automata are widely used and studied, many
Chapter 2
Finite Automata
28
2.1 Introduction
Finite automata: a rst model of the notion of eective procedure.
(They also have many other applications).
The concept of nite automaton can be derived
AN INTRODUCTION TO MATHEMATICAL PROOFS NOTES FOR MATH 3034
Jimmy T. Arnold
1
TABLE OF CONTENTS CHAPTER 1: The Structure of Mathematical Statements 1.1. Statements 1.2. Statement Forms, Logical Equiva
Trees and structural induction
Margaret M. Fleck
25 October 2010
These notes cover trees, tree induction, and structural induction. (Sections 10.1, 4.3 of Rosen.)
1
Why trees?
Computer scientists are
Finite Automata
Finite Automata
Two types both describe what are called regular languages
Deterministic (DFA) There is a fixed number of states and we can only be in one state at a time Nondetermini
CHAPTER 6
Proof by Contradiction
e now explore a third method of proof: proof by contradiction.
This method is not limited to proving just conditional statements
it can be used to prove any kind of st
Deterministic Finite State Automata
Sipser pages 31-46
Deterministic Finite Automata (DFA)
DFAs are easiest to present pictorially:
1
Q0
1
0
Q1
0
Q2
0,1
They are directed graphs whose nodes are state
CS5371
Theory of Computation
Lecture 3: Automata Theory I
(DFA and NFA)
Objectives
This time, we will look at how to
define a very simple
computer
called
deterministic finite automaton (DFA)
Show tha
PROOF BY
CONTRADICTION
proof by contradiction
Let r be a proposition.
A proof of r by contradiction consists of
proving that not(r) implies a contradiction,
thus concluding that not(r) is false,
which