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 = {q 1, q 2, q 3 }S = q 1 F = {q 2 } δ= {(q 1, 0, q 1 ), (q 1, 1, q 2 ), (q 2, 1, q 2 ), (q 2, 0, q 3 ), (q 3, 0, q 2 ), (q 3, 1, q 2 )}

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 = {q 1, q 2, q 3 }S = q 1 F = {q 3 } δ= {(q 1, 0, q 2 ), (q 1, 1, q 1 ), (q 2, 0, q 2 ), (q 2, 1, q 3 ), (q 3, 0, q 3 ), (q 3, 1, q 3 )}

Question 2 What language does this automata “accept?” M = (Q, Ʃ, δ, S, F) Ʃ = {0, 1} Q = {q 1, q 2, q 3 }S = q 1 F = {q 3 } δ= {(q 1, 0, q 2 ), (q 1, 1, q 1 ), (q 2, 0, q 2 ), (q 2, 1, q 3 ), (q 3, 0, q 3 ), (q 3, 1, q 3 )}

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

Examples

Regular Operations Closure

Regular Operations Closure

Regular Operations Closure

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

DFA  Regular Expression (RE)