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

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

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)}

Example 2

• What language does this describe?

Example 2

• Write this automata using set and sequence notation.

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)}

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)}

Question 3

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

Question 4

• What language does this automata accept

Question 5

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

Regular Languages

Regular Operations

Regular Operations

• Examples

Regular Operations

• Closure

Regular Operations

• Closure

Regular Operations

• Closure

Regular Expression Examples

Regular Expression Examples

Regular Expression (RE) NFA

• (ab ᴜ a)*

Regular Expression (RE) NFA

• (ab ᴜ a)*

Regular Expression (RE) NFA

• (a ᴜ b)*aba

(a ᴜ b)*aba

DFA Regular Expression (RE)

DFA Regular Expression (RE)

DFA Regular Expression (RE)

DFA Regular Expression (RE)

DFA Regular Expression (RE)

DFA Regular Expression (RE)

DFA Regular Expression (RE)

DFA Regular Expression (RE)

DFA Regular Expression (RE)

DFA Regular Expression (RE)