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  • Slide 1
  • Costas Busch - RPI1 Finite Automata
  • Slide 2
  • Costas Busch - RPI2 Finite Automaton Input String Output String Finite Automaton
  • Slide 3
  • Costas Busch - RPI3 Finite Accepter Input Accept or Reject String Finite Automaton Output
  • Slide 4
  • Costas Busch - RPI4 Transition Graph initial state final state accept state transition Abba -Finite Accepter
  • Slide 5
  • Costas Busch - RPI5 Initial Configuration Input String
  • Slide 6
  • Costas Busch - RPI6 Reading the Input
  • Slide 7
  • Costas Busch - RPI7
  • Slide 8
  • 8
  • Slide 9
  • 9
  • Slide 10
  • 10 Output: accept Input finished
  • Slide 11
  • Costas Busch - RPI11 Rejection
  • Slide 12
  • Costas Busch - RPI12
  • Slide 13
  • Costas Busch - RPI13
  • Slide 14
  • Costas Busch - RPI14
  • Slide 15
  • Costas Busch - RPI15 Output: reject Input finished
  • Slide 16
  • Costas Busch - RPI16 Another Rejection
  • Slide 17
  • Costas Busch - RPI17 Output: reject
  • Slide 18
  • Costas Busch - RPI18 Another Example
  • Slide 19
  • Costas Busch - RPI19
  • Slide 20
  • Costas Busch - RPI20
  • Slide 21
  • Costas Busch - RPI21
  • Slide 22
  • Costas Busch - RPI22 Output: accept Input finished
  • Slide 23
  • Costas Busch - RPI23 Rejection
  • Slide 24
  • Costas Busch - RPI24
  • Slide 25
  • Costas Busch - RPI25
  • Slide 26
  • Costas Busch - RPI26
  • Slide 27
  • Costas Busch - RPI27 Output: reject Input finished
  • Slide 28
  • Costas Busch - RPI28 Formalities Deterministic Finite Accepter (DFA) : set of states : input alphabet : transition function : initial state : set of final states
  • Slide 29
  • Costas Busch - RPI29 Input Alphabet
  • Slide 30
  • Costas Busch - RPI30 Set of States
  • Slide 31
  • Costas Busch - RPI31 Initial State
  • Slide 32
  • Costas Busch - RPI32 Set of Final States
  • Slide 33
  • Costas Busch - RPI33 Transition Function
  • Slide 34
  • Costas Busch - RPI34
  • Slide 35
  • Costas Busch - RPI35
  • Slide 36
  • Costas Busch - RPI36
  • Slide 37
  • Costas Busch - RPI37 Transition Function
  • Slide 38
  • Costas Busch - RPI38 Extended Transition Function
  • Slide 39
  • Costas Busch - RPI39
  • Slide 40
  • Costas Busch - RPI40
  • Slide 41
  • Costas Busch - RPI41
  • Slide 42
  • Costas Busch - RPI42 Observation: There is a walk from to with label
  • Slide 43
  • Costas Busch - RPI43 Example: There is a walk from to with label
  • Slide 44
  • Costas Busch - RPI44 Recursive Definition
  • Slide 45
  • Costas Busch - RPI45
  • Slide 46
  • Costas Busch - RPI46 Languages Accepted by DFAs Take DFA Definition: The language contains all input strings accepted by = { strings that drive to a final state}
  • Slide 47
  • Costas Busch - RPI47 Example accept
  • Slide 48
  • Costas Busch - RPI48 Another Example accept
  • Slide 49
  • Costas Busch - RPI49 Formally For a DFA Language accepted by :
  • Slide 50
  • Costas Busch - RPI50 Observation Language rejected by :
  • Slide 51
  • Costas Busch - RPI51 More Examples accept trap state
  • Slide 52
  • Costas Busch - RPI52 = { all strings with prefix } accept
  • Slide 53
  • Costas Busch - RPI53 = { all strings without substring }
  • Slide 54
  • Costas Busch - RPI54 Regular Languages A language is regular if there is a DFA such that All regular languages form a language family
  • Slide 55
  • Costas Busch - RPI55 { all strings with prefix } { all strings without substring } Examples of regular languages: There exist automata that accept these Languages (see previous slides).
  • Slide 56
  • Costas Busch - RPI56 Another Example The language is regular:
  • Slide 57
  • Costas Busch - RPI57 There exist languages which are not Regular: There is no DFA that accepts such a language (we will prove this later in the class) Example:

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