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Finite Automata

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.

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Finite Automata

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  1. Finite Automata Chapter 1

  2. Automatic Door Example • Top View

  3. Automatic Door Example • State diagram • State table

  4. Finite Automata  Markov Chain • Simple 2-state probabilistic Markov Chain

  5. Example 1 • What strings does this language “accept”

  6. Example 1 • Can you describe this language using set notation or a formal description?

  7. 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)}

  8. Example 2 • What language does this describe?

  9. Example 2 • Write this automata using set and sequence notation.

  10. 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)}

  11. 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)}

  12. Question 3 • Design an automata that will only accept binary strings that end with 0.

  13. Question 4 • What language does this automata accept

  14. Question 5 • Design an automata that only accepts strings that start and end with a different symbol, assume the alphabet is {a, b}

  15. Regular Languages

  16. Regular Operations

  17. Regular Operations • Examples

  18. Regular Operations • Closure

  19. Regular Operations • Closure

  20. Regular Operations • Closure

  21. Regular Expression Examples

  22. Regular Expression Examples

  23. Regular Expression (RE)  NFA • (ab ᴜ a)*

  24. Regular Expression (RE)  NFA • (ab ᴜ a)*

  25. Regular Expression (RE)  NFA • (a ᴜ b)*aba

  26. (a ᴜ b)*aba

  27. DFA  Regular Expression (RE)

  28. DFA  Regular Expression (RE)

  29. DFA  Regular Expression (RE)

  30. DFA  Regular Expression (RE)

  31. DFA  Regular Expression (RE)

  32. DFA  Regular Expression (RE)

  33. DFA  Regular Expression (RE)

  34. DFA  Regular Expression (RE)

  35. DFA  Regular Expression (RE)

  36. DFA  Regular Expression (RE)

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