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 L04 FSA: Non-deterministic FSA - Intro


              FSA:  Non-determinism

o  So far, transition matrix is a function, i.e., a unique state
   in any transition from any state.  Called deterministic FSA
   (DFSM or DFSA or DFA).

o  A FSM in which more than one transition possible from any one
   of the states is called non-deterministic FSM (NFSM or NFSA).
    +  Ex.: An NDFA for dates in Feb.

                           one
                           ...
                          twenty                               
                      ------>------
                     /             \
              Feb   /               \
       ->(q0)-->--(q1)-->--(q2)-->--((q3))
                      twenty    one
                                ...
                                nine

    -  Note:  From state q1, two possible transitions on input of
       'twenty' (to q2 or q3). Therefore, NFSA.
    -  Why have NFSA?  Ans:  Easier to build NFSA for some problems.
       Humans do case analysis, but the cases may not be disjoint.
       Leads to non-determinism.

o  Meaning:  If it is possible to reach an accepting state (through
   some path) for an input, accept the input.

                           one
                  ---------->---------
                  |        ...       |
                  |       twenty     |       0                 
                  |   ------>-----\  |  ---->----
                  |  /             \ | /         \
              Feb |/                \|/    2001    \
       ->(q0)-->--(q1)-->--(q2)-->--((q3))-->---- (q4)
                   \  twenty  | one  |              ^
                     \        | ...  |              /  
                       \      |-->---|             /
                         \      nine              /
                           \                     /
                             \-------->---------/
                                     2001

o  Empty transition:  Also leads to NFSA
    - Empty transition is an arc labelled with the empty string
      (i.e., 0)
    * Meaning: Without consuming any input, the machine can follow
      the transition arc.

    + Ex.:   %% To put an example %%
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