3

So I can take a given NFA with a single start state and convert it into an equivalent DFA quite easily, however I'm stumped when it comes to an NFA with multiple start states.

Since a DFA can only have one start state (if I'm correct) how do I know which of the two start states in the NFA becomes the sole start state in the DFA.

For reference, this is the NFA I'm trying to convert:

   N|   a   |   b   |   c   |
____________________________
 ->0| {0,2} | {0,3} |  ---  |
*->0|  {0}  |  {0}  |  {3}  |
   0|  {2}  |  ---  | {2,3} |
 * 0|  {2}  |  ---  |  {3}  |

Where: -> = initial state, * = accepting state, --- = empty set,

fletch254
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1 Answers1

6

A NFA with multiple start states is equivalent to a NFA with an additional state (which becomes the new, single start state) and ϵ-edges from that to the "actual" start states:

   N|   a   |   b   |   c   |   ϵ   |
----+-------+-------+-------+-------+
   0| {0,2} | {0,3} |   {}  |   {}  |
*  1|  {0}  |  {0}  |  {3}  |   {}  |
   2|  {2}  |   {}  | {2,3} |   {}  |
*  3|  {2}  |   {}  |  {3}  |   {}  |
 ->4|   {}  |   {}  |   {}  | {0,1} |
Bergi
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