CSE 311 Foundations of Computing I

Lecture 23Finite State Machines

Autumn 2012

Autumn 2012 CSE 311 1

Announcements

• Reading assignments– 7th Edition, Sections 13.3 and 13.4– 6th Edition, Section 12.3 and 12.4– 5th Edition, Section 11.3 and 11.4

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Lecture highlights:Database and relations

ID_Number Course

328012098 CSE311

328012098 CSE351

481080220 CSE311

238082388 CSE312

238082388 CSE344

238082388 CSE351

1727017 CSE312

348882811 CSE311

348882811 CSE312

348882811 CSE344

348882811 CSE351

2921938 CSE351

Databases consist of collection of n-ary relations

Student_Name ID_Number Office GPA

Knuth 328012098 022 4.00

Von Neuman 481080220 555 3.78

Russell 238082388 022 3.85

Einstein 238001920 022 2.11

Newton 1727017 333 3.61

Karp 348882811 022 3.98

Bernoulli 2921938 022 3.21

STUDENTTAKES

Relational algebra:

4

Relational Databases: Keys• An attribute is a key if all its values in the

database are always distinct

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Which attribute is the key?Why is Student_Name not a key?

Student_Name ID_Number Office GPA

Knuth 328012098 022 4.00

Von Neuman 481080220 555 3.78

Russell 238082388 022 3.85

Einstein 238001920 022 2.11

Newton 1727017 333 3.61

Karp 348882811 022 3.98

Bernoulli 2921938 022 3.21

5

Relational Databases: Relationships

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WORKS_ON is a relationship between students and project

Student_Name ID_Number Office

Knuth 328012098 022

Von Neuman 481080220 555

Russell 238082388 022

Einstein 238001920 022

Newton 1727017 333

Karp 348882811 022

Bernoulli 2921938 022

PRJ_ID Project_Name Due_date

P331 “Flying cyphers” 11/2012

P004 “Virtual induction” 12/2012

P901 “Binary bots” 12/2012

STUDENT

PROJECT

ID_Number PRJ_ID

2921938 P004

2921938 P901

1727017 P901Who works on what?

6

Types of Relationshipsin Relational Databases

• one-one:

• many-one

• many-many

123

abcd

123

abcd

123

abcd

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What type is WORKS_ON?

ID_Number PRJ_ID

2921938 P004

2921938 P901

1727017 P901

Finite state machines

StatesTransitions on inputsStart state and final statesThe language recognized by a machine is the set of strings that reach a final state

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s0 s2 s3s1111

0,1

0

0

0State 0 1

s0 s0 s1

s1 s0 s2

s2 s0 s3

s3 s3 s3

Applications of Finite State Machines (a.k.a. Finite Automata)

• Implementation of regular expression matching in programs like grep

• Control structures for sequential logic in digital circuits

• Algorithms for communication and cache-coherence protocols– Each agent runs its own FSM

• Design specifications for reactive systems– Components are communicating FSMs

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Applications of Finite State Machines (a.k.a. Finite Automata)

• Formal verification of systems– Is an unsafe state reachable?

• Computer games– FSMs provide worlds to explore

• Minimization algorithms for FSMs can be extended to more general models used in– Text prediction– Speech recognition

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What language does this machine recognize?

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s0

s2 s3

s1

1

1

1

1

0

0

0

0

3 Bit Shift register

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001 011

111

110

101010000

100

1

11 0 1

1

1

1

000 1

0

0

00

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001 011

111

110

101010000

100

1

11 0 1

1

1

1

000 1

0

0

00

10

00 01 10 11

11

1

0

0 0

0 0 0 01

1

1

1

Design a DFA that accepts strings with a 1 three positions from the end

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How does the size of a DFA to recognize “10th character is a 1” compare with the size of a DFA to recognize “10th character from the end is 1”?

Strings over {0, 1, 2}*

M1: Strings with an even number of 2’s

M2: Strings where the sum of digits mod 3 is 0

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s0 s1

t0 t2

t1

Recognize strings with an even number of 2’s and a mod 3 sum of 0

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s0t0

s1t0

s1t2

s0t1

s0t2

s1t1

State machines with output

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Input Output

State L R

s1 s1 s2 Beep

s2 s1 s3

s3 s2 s4

s4 s3 s4 Beep

S3 S4S1 S2

R

L

R

L

R

L

L

R

“Tug-of-war”

Vending Machine

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Enter 15 cents in dimes or nickelsPress S or B for a candy bar

Vending Machine, Version 1

0 5 10 15

D D

N N N, D

B, S

Basic transitions on N (nickel), D (dime), B (butterfinger), S (snickers)

Vending Machine, Version 2

0’ B 5 10

15

Adding output to states: N – Nickel, S – Snickers, B – Butterfinger

15’ N

0

0” S

N

N

N

N

N

B

D

D

D

D

D B

S

S

Vending Machine, Final Version

0’ B 5 10

15

Adding additional “unexpected” transitions

15’ N

0

0” S

N

N

N

N

N

B

D

D

D

D

D B

S

S

15”

DS

B

B,S

B,S

B,S

B,S B,S

N

N

N

D

D

D