costas busch - rpi1 finite automata. costas busch - rpi2 finite automaton input string output string...
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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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