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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 lifechanging software built with Microsoft tools and tec
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 propositional formulas (i.e., Statements) that return
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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 applications only use nite languages. Cover automata we
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 by examining what
happens when a program is executed on
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 Equivalence, and Negations 1.3. Quantiers 1.4: Denitions CHAP
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 obsessed with trees, because trees of various sorts
sho
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 Nondeterministic (NFA) There is a fixed number of states but we can
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 statement whatsoever. The basic idea
is to assume that th
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 states and whose arcs
are labeled by one or more symbols fro
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 that DFA can solve some string
decision problem
Then, we g
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 implies that r is true.
proof by contradiction
In part