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1 Finite Automata
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2 Finite Automaton Input “Accept” or “Reject” String Finite Automaton Output
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3 Transition Graph initial state accepting state transition
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4 Initial Configuration Input String
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5 Reading the Input
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9 accept Input finished
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10 Rejection
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14 reject Input finished
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15 Another Rejection
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16 reject
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17 Another Example
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21 accept Input finished
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22 Rejection Example
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26 reject Input finished
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27 Languages Accepted by FAs FA Definition: The language contains all input strings accepted by = { strings that bring to an accepting state}
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28 Example accept
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29 Example accept
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30 Example accept trap state
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31 Formal Definition Finite Automaton (FA) : set of states : input alphabet : transition function : initial state : set of accepting states
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32 Input Alphabet
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33 Set of States
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34 Initial State
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35 Set of Accepting States
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36 Transition Function
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40 Transition Function
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41 Extended Transition Function
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45 Observation: if there is a walk from to with label then
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46 Example: There is a walk from to with label
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47 Recursive Definition
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49 Language Accepted by FAs For a FA Language accepted by :
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50 Observation Language rejected by :
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51 Example = { all strings with prefix } accept
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52 Example = { all strings without substring }
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53 Example
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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
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55 { all strings with prefix } { all strings without substring } Examples of regular languages: There exist automata that accept these Languages (see previous slides).
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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:
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