An Introduction to the Theory of
Eitan Gurari, Ohio State University
Computer Science Press, 1989, ISBN 0-7167-8182-4
Copyright Eitan M. Gurari
To Shaula, Inbal, Itai, Erez, Netta, and Danna
1 GENERAL CONCEPTS
1.1 Alphabets, Strings, a
Introduction to Theory of Computation
School of Computer Science
April 11, 2016
1.1 Purpose and motivation . . .
Lecture 5 September 17
A Language is a set of strings over an alphabet
A DFA is deterministic for each state. It can process each character in only one way. It is finite meaning it
has a finite number of states and a finite alph
Countably Infinite set theorems
If A is a countably infinite set and B is an infinite subset of A then B is countable.
If A & B are countably infinite sets then A X B are countably infinite.
This is proved using Cantors Diagonal argumen
Alphabet is non-empty finite set of symbols.
We will generally denote an alphabet using sigma
This class is about whether or not something can be computed not whether the computation is effici
Basic Set Theory
Sets: which of the following are sets?
cfw_1, 1, 2, 3, 5, 8, 13, 21,
cfw_1, -1, 2, -2, 3, -3, 4, -4,
The first is not a set since it doesnt have unique elements
The second is since all of its elements are unique
Lecture 4 September 8
Cantors Theorem from Wikipedia:
Suppose that N is equinumerous with its power set P(N). Let us see a sample of what P(N) looks like:
P(N) contains infinite subsets of N, e.g. the set of all even numbers cfw_2, 4, 6,., as wel