1. Fall 2004COMP 3351 Finite Automata

2. Fall 2004COMP 3352 Finite Automaton Input String Output String Finite Automaton

3. Fall 2004COMP 3353 Finite Accepter Input “Accept” or “Reject” String Finite Automaton Output

4. Fall 2004COMP 3354 Transition Graph initial state final state “accept” state transition abba - Finite Accepter

5. Fall 2004COMP 3355 Initial Configuration Input String

6. Fall 2004COMP 3356 Reading the Input

7. Fall 2004COMP 3357

8. Fall 2004COMP 3358

9. Fall 2004COMP 3359

10. Fall 2004COMP 33510 Output: “accept” Input finished

11. Fall 2004COMP 33511 Rejection

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15. Fall 2004COMP 33515 Output: “reject” Input finished

16. Fall 2004COMP 33516 Another Rejection

17. Fall 2004COMP 33517 Output: “reject”

18. Fall 2004COMP 33518 Another Example

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22. Fall 2004COMP 33522 Output: “accept” Input finished

23. Fall 2004COMP 33523 Rejection

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27. Fall 2004COMP 33527 Output: “reject” Input finished

28. Fall 2004COMP 33528 Formalities Deterministic Finite Accepter (DFA) : (A finite) set of states : (A finite) set of input alphabet : transition function : initial state (an element of Q) : set of final states (a subset of Q )

29. Fall 2004COMP 33529 Input Alphabet

30. Fall 2004COMP 33530 Set of States

31. Fall 2004COMP 33531 Initial State

32. Fall 2004COMP 33532 Set of Final States

33. Fall 2004COMP 33533 Transition Function

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37. Fall 2004COMP 33537 Transition Function

38. Fall 2004COMP 33538 Extended Transition Function

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42. Fall 2004COMP 33542 Observation: There is a walk from to with label

43. Fall 2004COMP 33543 Example: There is a walk from to with label

44. Fall 2004COMP 33544 Recursive Definition

45. Fall 2004COMP 33545

46. Fall 2004COMP 33546 Languages Accepted by DFAs Take DFA Definition: The language contains all input strings accepted by = { strings that drive to a final state}

47. Fall 2004COMP 33547 Example accept

48. Fall 2004COMP 33548 Another Example accept

49. Fall 2004COMP 33549 Formally For a DFA Language accepted by :

50. Fall 2004COMP 33550 Observation Language rejected by :

51. Fall 2004COMP 33551 More Examples accept trap state

52. Fall 2004COMP 33552 = { all strings with prefix } accept

53. Fall 2004COMP 33553 = { all strings without substring }

54. Fall 2004COMP 33554 Regular Languages A language is regular if there is a DFA such that All regular languages form a language family

55. Fall 2004COMP 33555 { all strings with prefix } { all strings with suffix } { all strings without substring } Examples of regular languages: There exist automata that accept these Languages (see previous slides).

56. Fall 2004COMP 33556 Another Example The language is regular:

57. Fall 2004COMP 33557 There exist languages which are not Regular: There is no DFA that accepts such a language (we will prove this later!) Example: