Formal Languages Finite Automata Finite Automaton Input String
- Slides: 64
Formal Languages Finite Automata
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
Acceptance or Rejection? 15
Initial State 16
Rejection reject 17
Language? 18
Another Example 19
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Input finished accept 23
Rejection Example 24
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Input finished reject 28
Languages Accepted by FAs FA Definition: The language contains all input strings accepted by = { strings that bring to an accepting state} 29
Example: L(M) = ? accept 30
Example accept 31
Example: L(M) = ? accept 32
Example accept 33
Example: L(M) = ? accept trap state 34
Example accept trap state 35
Formal Definition Finite Automaton (FA) : set of states : input alphabet : transition function : initial state : set of accepting states 36
Input Alphabet 37
Set of States 38
Initial State 39
Set of Accepting States 40
Transition Function 41
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Transition Function 45
Extended Transition Function 46
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Observation: if there is a walk from with label then to 50
Example: There is a walk from with label to 51
Recursive Definition 52
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Language Accepted by FAs For a FA Language accepted by : 54
Observation Language rejected by : 55
L(M) ? accept 56
Example = { all strings with prefix } accept 57
L(M)? 58
Example = { all strings without substring } 59
L(M) ? 60
Example 61
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 62
Examples of regular languages: { all strings with prefix } { all strings without substring } There exist automata that accept these Languages (see previous slides). 63
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) 64