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 L04 FSA: Combining FSAs: Concatenation


                  Combining FSAs:  Concatenation

o  Given a large problem, sub-divide into smaller tasks.  Have a 
   FSA for each task.  Then combine the FSAs:

o  Concatenation of strings in two languages
       s in Ls
       t in Lt
   Combination of the two gives a new language:
       Lnew =  { s.t | s in Ls, and t in Lt }
   where s.t is concatenation of strings s and t

o  Concatenating FSAs:  Fs and Ft for above languages
    Fs:
      ->(qs0)->-  ...  ((qs))
                  ...  ((qs'))

    Ft: 
      ->(qt0)->-  ...  ((qt))
                  ...  ((qt'))
                  ...  ((qt"))

   After concatenation, New FSA:
                           0
     ->(qs0)-> ...   (qs)->-- (qt0) -> ... ((qt))
                               /       ... ((qt'))
                              /        ... ((qt"))
                  .. (qs') ->/ 0


    * Connected with 0-transitions from accepting states of Fs
      to initial state of Ft.  Other transitions same as before.

    - New initial state: qs0
    - New accepting states: qt, qt', qt"

+  Ex.: A quantity followed by units like in: 
           thirty five kilometres per hour
    - Define FSA for quantity,
    - Another for units
    * Concatenate them

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