Finite Automata Chapter 1. Automatic Door Example Top View.

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)*


• (ab ᴜ a)*


• (a ᴜ b)*aba

(a ᴜ b)*aba

DFA Regular Expression (RE)










Finite Automata Chapter 1. Automatic Door Example Top View.

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