[PPT] - Automata Theory Why Study Automata? What the Course is About 1 PowerPoint Presentation

SLIDE 1

1

Automata Theory

Why Study Automata? What the Course is About

SLIDE 2

2

Why Study Automata?

A survey of Stanford grads 5 years out asked which of their courses did they use in their job. Basics like intro-programming took the top spots, of course. But among optional courses, CS154 stood remarkably high.

3X the score for AI, for example.

SLIDE 3

3

How Could That Be?

Regular expressions are used in many systems.

E.g., UNIX a.b. E.g., DTD’s describe XML tags with a RE format like person (name, addr, child).

Finite automata model protocols, electronic circuits.

SLIDE 4

4

How? – (2)

Context-free grammars are used to describe the syntax of essentially every programming language.

Not to forget their important role in describing natural languages.

And DTD’s taken as a whole, are really CFG’s.

SLIDE 5

5

How? – (3)

When developing solutions to real problems, we often confront the limitations of what software can do.

Undecidable things – no program whatever can do it. Intractable things – there are programs, but no fast programs.

Automata theory gives you the tools.

SLIDE 6

6

Other Good Stuff

We’ll learn how to deal formally with discrete systems.

Proofs: You never really prove a program correct, but you need to be thinking of why a tricky technique really works.

We’ll gain experience with abstract models and constructions.

Models layered software architectures.

SLIDE 7

7

Automata Theory – Gateway Drug

This theory has attracted people of a mathematical bent to CS, to the betterment of all.

Ken Thompson – before UNIX was working

n compiling regular expressions.

Jim Gray – thesis was automata theory before he got into database systems and made fundamental contributions there.

SLIDE 8

8

Course Outline

Regular Languages and their descriptors:

Finite automata, nondeterministic finite automata, regular expressions. Algorithms to decide questions about regular languages, e.g., is it empty? Closure properties of regular languages.

SLIDE 9

9

Course Outline – (2)

Context-free languages and their descriptors:

Context-free grammars, pushdown automata. Decision and closure properties.

SLIDE 10

10

Course Outline – (3)

Recursive and recursively enumerable languages.

Turing machines, decidability of problems. The limit of what can be computed.

Intractable problems.

Problems that (appear to) require exponential time. NP-completeness and beyond.

SLIDE 11

11

Finite Automata

What Are They? Who Needs ‘em? An Example: Scoring in Tennis

SLIDE 12

12

What is a Finite Automaton?

A formal system. Remembers only a finite amount of information. Information represented by its state. State changes in response to inputs. Rules that tell how the state changes in response to inputs are called transitions.

SLIDE 13

13

Why Study Finite Automata?

Used for both design and verification of circuits and communication protocols. Used for many text-processing applications. An important component of compilers. Describes simple patterns of events, etc.

SLIDE 14

14

Tennis

Like ping-pong, except you are very tiny and stand on the table. Match = 3-5 sets. Set = 6 or more games.

SLIDE 15

15

Scoring a Game

One person serves throughout. To win, you must score at least 4 points. You also must win by at least 2 points. Inputs are s = “server wins point” and o = “opponent wins point.”

SLIDE 16

16

Love Start Love-15 15-Love s

Love-30

15-all 30-Love s s

Love-40

15-30 30-15 40-Love s s s

Server

Wins Opp’nt Wins s

40-15

15-40 30-all s s s

30-40

40-30 s s s

deuce

s s

Ad-out

Ad-in s

s
s

SLIDE 17

17

Acceptance of Inputs

Given a sequence of inputs (input string ), start in the start state and follow the transition from each symbol in turn. Input is accepted if you wind up in a final (accepting) state after all inputs have been read.

SLIDE 18

18

Example: Processing a String

Love Start Love-15 15-Love s

Love-30

15-all 30-Love s s

Love-40

15-30 30-15 40-Love s s s

Server

Wins Opp’nt Wins s

40-15

15-40 30-all s s s

30-40

40-30 s s s

deuce

s s

Ad-out

Ad-in s

s
s
s o s o s o s o s o s s

*

SLIDE 19

19

Example: Processing a String

Love Start Love-15 15-Love s

Love-30

15-all 30-Love s s

Love-40

15-30 30-15 40-Love s s s

Server

Wins Opp’nt Wins s

40-15

15-40 30-all s s s

30-40

40-30 s s s

deuce

s s

Ad-out

Ad-in s

s
s
s o s o s o s o s o s s

*

SLIDE 20

20

Example: Processing a String

Love Start Love-15 15-Love s

Love-30

15-all 30-Love s s

Love-40

15-30 30-15 40-Love s s s

Server

Wins Opp’nt Wins s

40-15

15-40 30-all s s s

30-40

40-30 s s s

deuce

s s

Ad-out

Ad-in s

s
s
s o s o s o s o s o s s

*

SLIDE 21

21

Example: Processing a String

Love Start Love-15 15-Love s

Love-30

15-all 30-Love s s

Love-40

15-30 30-15 40-Love s s s

Server

Wins Opp’nt Wins s

40-15

15-40 30-all s s s

30-40

40-30 s s s

deuce

s s

Ad-out

Ad-in s

s
s
s o s o s o s o s o s s

*

SLIDE 22

22

Example: Processing a String

Love Start Love-15 15-Love s

Love-30

15-all 30-Love s s

Love-40

15-30 30-15 40-Love s s s

Server

Wins Opp’nt Wins s

40-15

15-40 30-all s s s

30-40

40-30 s s s

deuce

s s

Ad-out

Ad-in s

s
s
s o s o s o s o s o s s

*

SLIDE 23

23

Example: Processing a String

Love Start Love-15 15-Love s

Love-30

15-all 30-Love s s

Love-40

15-30 30-15 40-Love s s s

Server

Wins Opp’nt Wins s

40-15

15-40 30-all s s s

30-40

40-30 s s s

deuce

s s

Ad-out

Ad-in s

s
s
s o s o s o s o s o s s

*

SLIDE 24

24

Example: Processing a String

Love Start Love-15 15-Love s

Love-30

15-all 30-Love s s

Love-40

15-30 30-15 40-Love s s s

Server

Wins Opp’nt Wins s

40-15

15-40 30-all s s s

30-40

40-30 s s s

deuce

s s

Ad-out

Ad-in s

s
s
s o s o s o s o s o s s

*

SLIDE 25

25

Example: Processing a String

Love Start Love-15 15-Love s

Love-30

15-all 30-Love s s

Love-40

15-30 30-15 40-Love s s s

Server

Wins Opp’nt Wins s

40-15

15-40 30-all s s s

30-40

40-30 s s s

deuce

s s

Ad-out

Ad-in s

s
s
s o s o s o s o s o s s

*

SLIDE 26

26

Example: Processing a String

Love Start Love-15 15-Love s

Love-30

15-all 30-Love s s

Love-40

15-30 30-15 40-Love s s s

Server

Wins Opp’nt Wins s

40-15

15-40 30-all s s s

30-40

40-30 s s s

deuce

s s

Ad-out

Ad-in s

s
s
s o s o s o s o s o s s

*

SLIDE 27

27

Example: Processing a String

Love Start Love-15 15-Love s

Love-30

15-all 30-Love s s

Love-40

15-30 30-15 40-Love s s s

Server

Wins Opp’nt Wins s

40-15

15-40 30-all s s s

30-40

40-30 s s s

deuce

s s

Ad-out

Ad-in s

s
s
s o s o s o s o s o s s

*

SLIDE 28

28

Example: Processing a String

Love Start Love-15 15-Love s

Love-30

15-all 30-Love s s

Love-40

15-30 30-15 40-Love s s s

Server

Wins Opp’nt Wins s

40-15

15-40 30-all s s s

30-40

40-30 s s s

deuce

s s

Ad-out

Ad-in s

s
s
s o s o s o s o s o s s

*

SLIDE 29

29

Example: Processing a String

Love Start Love-15 15-Love s

Love-30

15-all 30-Love s s

Love-40

15-30 30-15 40-Love s s s

Server

Wins Opp’nt Wins s

40-15

15-40 30-all s s s

30-40

40-30 s s s

deuce

s s

Ad-out

Ad-in s

s
s
s o s o s o s o s o s s

*

SLIDE 30

30

Example: Processing a String

Love Start Love-15 15-Love s

Love-30

15-all 30-Love s s

Love-40

15-30 30-15 40-Love s s s

Server

Wins Opp’nt Wins s

40-15

15-40 30-all s s s

30-40

40-30 s s s

deuce

s s

Ad-out

Ad-in s

s
s
s o s o s o s o s o s s

*

SLIDE 31

31

Language of an Automaton

The set of strings accepted by an automaton A is the language of A. Denoted L(A). Different sets of final states -> different languages. Example: As designed, L(Tennis) = strings that determine the winner.

SLIDE 32

32

Automata Theory

Why Study Automata? What the Course is About

Why Study Automata?

A survey of Stanford grads 5 years out asked which of their courses did they use in their job. Basics like intro-programming took the top spots, of course. But among optional courses, CS154 stood remarkably high.

3X the score for AI, for example.

How Could That Be?

Regular expressions are used in many systems.

E.g., UNIX a.*b. E.g., DTD’s describe XML tags with a RE format like person (name, addr, child*).

Finite automata model protocols, electronic circuits.

How? – (2)

Context-free grammars are used to describe the syntax of essentially every programming language.

Not to forget their important role in describing natural languages.

And DTD’s taken as a whole, are really CFG’s.

How? – (3)

When developing solutions to real problems, we often confront the limitations of what software can do.

Undecidable things – no program whatever can do it. Intractable things – there are programs, but no fast programs.

Automata theory gives you the tools.

Other Good Stuff

We’ll learn how to deal formally with discrete systems.

Proofs: You never really prove a program correct, but you need to be thinking of why a tricky technique really works.

We’ll gain experience with abstract models and constructions.

Models layered software architectures.

Automata Theory – Gateway Drug

This theory has attracted people of a mathematical bent to CS, to the betterment of all.

Ken Thompson – before UNIX was working

Jim Gray – thesis was automata theory before he got into database systems and made fundamental contributions there.

Course Outline

Regular Languages and their descriptors:

Finite automata, nondeterministic finite automata, regular expressions. Algorithms to decide questions about regular languages, e.g., is it empty? Closure properties of regular languages.

Course Outline – (2)

Context-free languages and their descriptors:

Context-free grammars, pushdown automata. Decision and closure properties.

Course Outline – (3)

Recursive and recursively enumerable languages.

Turing machines, decidability of problems. The limit of what can be computed.

Intractable problems.

Problems that (appear to) require exponential time. NP-completeness and beyond.

Finite Automata

What Are They? Who Needs ‘em? An Example: Scoring in Tennis

What is a Finite Automaton?

A formal system. Remembers only a finite amount of information. Information represented by its state. State changes in response to inputs. Rules that tell how the state changes in response to inputs are called transitions.

Why Study Finite Automata?

Used for both design and verification of circuits and communication protocols. Used for many text-processing applications. An important component of compilers. Describes simple patterns of events, etc.

Tennis

Like ping-pong, except you are very tiny and stand on the table. Match = 3-5 sets. Set = 6 or more games.

Scoring a Game

One person serves throughout. To win, you must score at least 4 points. You also must win by at least 2 points. Inputs are s = “server wins point” and o = “opponent wins point.”

Acceptance of Inputs

Given a sequence of inputs (input string ), start in the start state and follow the transition from each symbol in turn. Input is accepted if you wind up in a final (accepting) state after all inputs have been read.

Example: Processing a String

*

Example: Processing a String

*

Example: Processing a String

*

Example: Processing a String

*

Example: Processing a String

*

Example: Processing a String

*

Example: Processing a String

*

Example: Processing a String

*

Example: Processing a String

*

Example: Processing a String

*

Example: Processing a String

*

Example: Processing a String

*

Example: Processing a String

*

Language of an Automaton

The set of strings accepted by an automaton A is the language of A. Denoted L(A). Different sets of final states -> different languages. Example: As designed, L(Tennis) = strings that determine the winner.

Text (Not Required)

Hopcroft, Motwani, Ullman, Automata Theory, Languages, and Computation 3rd Edition. Course covers essentially the entire book.

E.g., UNIX a.b. E.g., DTD’s describe XML tags with a RE format like person (name, addr, child).