Formal Languages Finite Automata Dr.Hamed Alrjoub 1FA1

2 Wikipedia Chomsky Hierarchy FA1

3 Finite Automaton Input “Accept” or “Reject” String Finite Automaton Output FA1

4 Transition Graph initial state accepting state transition FA1

5 Initial Configuration Input String FA1

6 Reading the Input FA1

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10 accept Input finished FA1

11 Rejection FA1

12 FA1

13 FA1

14 FA1

15 reject Input finished FA1

16 Acceptance or Rejection? FA1

17 Initial State FA1

18 reject Rejection FA1

19 Language? FA1

20 Another Example FA1

21FA1

22FA1

23FA1

24 accept Input finished FA1

25 Rejection Example FA1

26FA1

27FA1

28FA1

29 reject Input finished FA1

30 Languages Accepted by FAs FA Definition: The language contains all input strings accepted by = { strings that bring to an accepting state} FA1

31 Example: L(M) = ? accept FA1

32 Example accept FA1

33 Example: L(M) = ? accept FA1

34 Example accept FA1

35 Example: L(M) = ? accept trap state FA1

36 Example accept trap state FA1

37 Formal Definition Finite Automaton (FA) : set of states : input alphabet : transition function : initial state : set of accepting states FA1

38 Input Alphabet FA1

39 Set of States FA1

40 Initial State FA1

41 Set of Accepting States FA1

42 Transition Function FA1

43 FA1

44 FA1

45FA1

46 Transition Function FA1

47 Extended Transition Function FA1

48FA1

49FA1

50FA1

51 Observation: if there is a walk from to with label then FA1

52 Example: There is a walk from to with label FA1

53 Recursive Definition FA1

54 FA1

55 Language Accepted by FAs For a FA Language accepted by : FA1

56 Observation Language rejected by : FA1

57 L(M) ? accept FA1

58 Example = { all strings with prefix } accept FA1

59 L(M)? FA1

60 Example = { all strings without substring } FA1

61 L(M) ? FA1

62 Example FA1

63 Regular Languages Definition: A language is regular if there is FA such that Observation: All languages accepted by FAs form the family of regular languages FA1

64 { all strings with prefix } { all strings without substring } Examples of regular languages: There exist automata that accept these Languages (see previous slides). FA1

65 There exist languages which are not Regular: There is no FA that accepts such a language (we will prove this later in the class) Example: FA1