finite automata

44
Finite Automata Chapter 1

Upload: abbott

Post on 14-Jan-2016

24 views

Category:

Documents


0 download

DESCRIPTION

Finite Automata. Chapter 1. Automatic Door Example. Top View. Automatic Door Example. State diagram State table. Finite Automata  Markov Chain. Simple 2-state probabilistic Markov Chain. Example 1. What strings does this language “accept”. Example 1. - PowerPoint PPT Presentation

TRANSCRIPT

Page 1: Finite Automata

Finite Automata

Chapter 1

Page 2: Finite Automata

Automatic Door Example

• Top View

Page 3: Finite Automata

Automatic Door Example

• State diagram

• State table

Page 4: Finite Automata

Finite Automata Markov Chain

• Simple 2-state probabilistic Markov Chain

Page 5: Finite Automata

Example 1

• What strings does this language “accept”

Page 6: Finite Automata

Example 1

• Can you describe this language using set notation or a formal description?

Page 7: Finite Automata

Example 1

• This machine can be describes using set and sequence notation.

M = (Q, Ʃ, δ, S, F) Ʃ = {0, 1} Q = {q1, q2, q3} S = q1

F = {q2}δ= {(q1, 0, q1), (q1, 1, q2), (q2, 1, q2), (q2, 0, q3),

(q3, 0, q2), (q3, 1, q2)}

Page 8: Finite Automata

Example 2

• What language does this describe?

Page 9: Finite Automata

Example 2

• Write this automata using set and sequence notation.

Page 10: Finite Automata

Question 1

• Draw this automata as a state diagram.

M = (Q, Ʃ, δ, S, F) Ʃ = {0, 1} Q = {q1, q2, q3} S = q1

F = {q3}δ= {(q1, 0, q2), (q1, 1, q1), (q2, 0, q2), (q2, 1, q3),

(q3, 0, q3), (q3, 1, q3)}

Page 11: Finite Automata

Question 2

• What language does this automata “accept?”

M = (Q, Ʃ, δ, S, F) Ʃ = {0, 1} Q = {q1, q2, q3} S = q1

F = {q3}δ= {(q1, 0, q2), (q1, 1, q1), (q2, 0, q2), (q2, 1, q3),

(q3, 0, q3), (q3, 1, q3)}

Page 12: Finite Automata

Question 3

• Design an automata that will only accept binary strings that end with 0.

Page 13: Finite Automata

Question 4

• What language does this automata accept

Page 14: Finite Automata

Question 5

• Design an automata that only accepts strings that start and end with a different symbol, assume the alphabet is {a, b}

Page 15: Finite Automata

Regular Languages

Page 16: Finite Automata

Regular Operations

Page 17: Finite Automata

Regular Operations

• Examples

Page 18: Finite Automata

Regular Operations

• Closure

Page 19: Finite Automata
Page 20: Finite Automata
Page 21: Finite Automata

Regular Operations

• Closure

Page 22: Finite Automata
Page 23: Finite Automata
Page 24: Finite Automata

Regular Operations

• Closure

Page 25: Finite Automata
Page 26: Finite Automata
Page 27: Finite Automata
Page 28: Finite Automata

Regular Expression Examples

Page 29: Finite Automata

Regular Expression Examples

Page 30: Finite Automata

Regular Expression (RE) NFA

• (ab ᴜ a)*

Page 31: Finite Automata

Regular Expression (RE) NFA

• (ab ᴜ a)*

Page 32: Finite Automata

Regular Expression (RE) NFA

• (a ᴜ b)*aba

Page 33: Finite Automata

(a ᴜ b)*aba

Page 34: Finite Automata

DFA Regular Expression (RE)

Page 35: Finite Automata

DFA Regular Expression (RE)

Page 36: Finite Automata

DFA Regular Expression (RE)

Page 37: Finite Automata

DFA Regular Expression (RE)

Page 38: Finite Automata

DFA Regular Expression (RE)

Page 39: Finite Automata

DFA Regular Expression (RE)

Page 40: Finite Automata

DFA Regular Expression (RE)

Page 41: Finite Automata

DFA Regular Expression (RE)

Page 42: Finite Automata

DFA Regular Expression (RE)

Page 43: Finite Automata

DFA Regular Expression (RE)

Page 44: Finite Automata