Formal Denition of a Nondeterministic Finite
Automaton
September 3, 2013
Formal Denition of a Nondeterministic Finite Automaton
A comment rst
The formal denition of an NFA is similar to that of a DFA.
Both have states, an alphabet, transition function, on
Formal Denition of a Finite Automaton
August 26, 2013
Formal Denition of a Finite Automaton
Why a formal denition?
A formal denition is precise:
- It resolves any uncertainties about what is allowed in a nite automaton such
as the number of accept states
Finite Automata: Informal
August 26, 2013
Finite Automata: Informal
Computational models
The theory of computation begins with the question:
what is a computer?
Real computers are however quite complicated so it is dicult
to set up a manageable mathematic
Denitions, Theorems, and Proofs
August 20, 2013
Denitions, Theorems, and Proofs
Note
The following three entities are central to every mathematical
subject, including the theory of computation.
Theorems are the heart of mathematics
Denitions, Theorems, an
Functions and Relations
August 19, 2013
Functions and Relations
Functions
A function is a mathematical object that sets up an
input-output relationship
A function takes an input and produces an output; in every
function the same input always produces the
Graphs, Strings, Languages and Boolean Logic
August 20, 2013
Graphs, Strings, Languages and Boolean Logic
Graphs
An undirected graph, or simple a graph, is a set of points with
lines connecting some points.
The points arecalled nodes or vertices, and the
Formal Denition of Computation
August 28, 2013
Formal Denition of Computation
Computation model
The model of computation considered so far is the work
performed by a nite automaton
Finite automata were described informally, using state
diagrams, and forma
The Regular Operations
August 28, 2013
The Regular Operations
Introduction
Once automata and computation have been dened, their
properties need be studied
The Regular Operations
Introduction
Once automata and computation have been dened, their
properties
Second Part of Regular Expressions Equivalence
with Finite Automata
September 11, 2013
Second Part of Regular Expressions Equivalence with Finite Aut
Lemma 1.60
If a language is regular then it is specied by a regular expression
Proof idea: For a given re
The Pumping Lemma for Regular Languages
September 15, 2013
The Pumping Lemma for Regular Languages
Nonregular languages
Consider the language B = cfw_0n 1n |n 0.
The Pumping Lemma for Regular Languages
Nonregular languages
Consider the language B = cfw_0n
Regular Expressions
September 11, 2013
Regular Expressions
Expressions
In arithmetic:
1. expressions are constructed from numbers and variables using
arithmetic operations and parantheses
2. expressions represent computations with numbers
3. results of ex
Closure under the Regular Operations
September 7, 2013
Closure under the Regular Operations
Application of NFA
Now we use the NFA to show that collection of regular
languages is closed under regular operations union,
concatenation, and star
Earlier we hav
Nondeterminism
September 3, 2013
Nondeterminism
Introduction
Nondeterminism is a useful concept that has a great impact
on the theory of computation
Nondeterminism
Introduction
Nondeterminism is a useful concept that has a great impact
on the theory of co
Mathematical Notions and Terminology
August 23, 2013
Mathematical Notions and Terminology
Sets
A set is a collection of objects represented as a unit.
The objects in a set are called elements or members.
Sets may be described formally by:
1. enumerating t