finite automata
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 PresentationTRANSCRIPT
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)