Finite Automata 1 Finite Automaton Input String Output

Finite Automata 1

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

Transition Graph initial state transition accepting state 3

Initial Configuration Input String 4

Reading the Input 5

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Input finished accept 9

Rejection 10

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Input finished reject 14

Another Rejection 15

reject 16

Another Example 17

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Input finished accept 21

Rejection Example 22

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Input finished reject 26

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

Example accept 28

Example accept 29

Example accept trap state 30

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

Input Alphabet 32

Set of States 33

Initial State 34

Set of Accepting States 35

Transition Function 36

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Transition Function 40

Extended Transition Function 41

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

Example: There is a walk from with label to 46

Recursive Definition 47

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

Observation Language rejected by : 50

Example = { all strings with prefix } accept 51

Example = { all strings without substring } 52

Example 53

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 54

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

There exist languages which are not Regular: Example: There is no FA that accepts such a language (we will prove this later in the class) 56