1 Finite Automata

2 Finite Automaton Input “Accept” or “Reject” String Finite Automaton Output

3 Transition Graph initial state accepting state transition

4 Initial Configuration Input String

5 Reading the Input

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9 accept Input finished

10 Rejection

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14 reject Input finished

15 Another Rejection

16 reject

17 Another Example

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21 accept Input finished

22 Rejection Example

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26 reject Input finished

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

28 Example accept

29 Example accept

30 Example accept trap state

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

32 Input Alphabet

33 Set of States

34 Initial State

35 Set of Accepting States

36 Transition Function

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40 Transition Function

41 Extended Transition Function

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

46 Example: There is a walk from to with label

47 Recursive Definition

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49 Language Accepted by FAs For a FA Language accepted by :

50 Observation Language rejected by :

51 Example = { all strings with prefix } accept

52 Example = { all strings without substring }

53 Example

54 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

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

56 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: