2/5/13
Kleenes Theorem
Kleenes Theorem
Models of Computa:on
Lecture #7
Chapter 7 introduced
Kleenes Theorem
Any language that be dened by a
regular expression,
nite automaton, or
transi:on graph
ca

2/17/13
Reviewing
Kleenes Theorem
Models of Computa:on
Lecture #10
Chapter 7 concluded
We can convert an RE to an FA for these cases:
individual leIers from
union of two REs
concatena:on of two REs

3/4/13
Regular Language
Regular Languages
Any language that can be described by a regular
expression is called a regular language
Models of Computa8on
Lecture #12 and 13
Chapter 9
Regular Language
Regular Lang

3/27/13
Machines and Languages
Pushdown Automata (PDA)
Models of Computa<on
Chapter 14
PDA is the machine for a CFL.
Quick observa<on
How can we compare the FA to the PDA?
Is one a more powerful machine

2/27/13
Extending capabili;es
Machines that can produce output
note that an FA can represent output via a
state, but we now mean explicit output
Two related models
Moore machine
Mealy machine
Finite Automata

3/25/13
All regular languages are CFLs
Construc+ve proof.
Convert an FA to a CFG.
Gramma+cal Format
Models of Computa+on
Chapter 13
FA CFG
Example: EVEN-EVEN to CFG
Let the name of the start state b

1/28/13
Another way to dene a language
Finite Automata
Models of Computa8on
Lecture #4
Chapter 5
Previously, we used deni8ons like:
L2 = cfw_ xn for n = 1 3 5 7
Then recursive deni8ons:
Rule 1.

3/20/13
Not all languages are regular
Previously we have proven, using the pumping
lemma, that not all languages are regular.
Context-Free Grammars
Models of Computa:on
Chapter 12
It turns out that there a

3/18/13
Regular Language
Recall, that any language that can be described
by a regular expression is called a regular
language
In this lecture we will prove that not all
languages are regular. That is, there are

Transi'on Graphs
Models of Computa'on
Lecture #5 (a;er quiz)
Chapter 6
Building a beCer mousetrap
Lets build an FA that only accepts the string
abba from = cfw_ a b
Building a beCer mousetrap
Lets build

2/13/13
Reviewing
Kleenes Theorem
Models of Computa9on
Lecture #9
Chapter 7 con9nued
We can convert an RE to an FA for these cases:
individual leIers from
union of two REs
S9ll to come:
concaten

1/31/13
Recall Transi+on Graphs
Transi+on Graphs
Models of Computa+on
Lecture #6
Chapter 6 concluded
Transi+on Graphs
Example: The language of all words that contain
a double leIer.
aa, bb
+
a, b
a, b

2/11/13
Remember me?
Kleenes Theorem
Now where was I?
Models of Computa9on
Lecture #8
Chapter 7 con9nued
Kleenes Theorem
Any language that be dened by a
regular expression,
nite automaton, or
tr

1/25/13
Another way to dene a language
Regular Expressions
Models of Computa;on
Lecture #3
Chapter 4
Previously, we used deni;ons like:
L2 = cfw_ xn for n = 1 3 5 7
or
L4 = cfw_ xn for n =

1/23/13
First: Unnished business
Recursive deni1ons
Models of Computa1on
Lecture #2
Chapter 3
Proof by Construc1on
S = cfw_ aa aaa
Prove, for n > 1, an is found in S*
Proof:
n = 2; an element of S, (