The DFA Minimizing option
The Minimize option gives guidance in building an equivalent
DFA with the minimum number of states. The minimize button is
located in the Options menu. Once a DFA is built, select the
"Minimize" option in the menubar. A new window will
appear in which you can start building the tree to find
undistinguishable states. When done with that window a second
window will appear in which you can build the minimized DFA.
Note that DFA's are supposed to have a transition leaving from
every state for each letter of the machine's alphabet. If any
transitions are omitted, then you will have an implicit trap
state in your automaton. This implicit state will be added as
your last state (but not shown in the Finite Automata window) and
will be treated in the tree as if it were in your machine (a
reminder will pop up when starting the tree if you have an
implicit trap state). This trap state will be removed in the
second minimizing window since it is only necessary for
distingishing states in the tree.
The Tree Window
The tree window will begin with the two trees (final and
nonfinal) already started. The final tree's root will contain a
label representing all the final states from the DFA and the
nonfinal tree's root will contain a label representing all
nonfinal states. For more help on how State labels work see the
"NFA to DFA" help. When you are done building the tree
click on the "Done" button. The next window will appear
if the tree is correct.In the tree window, all the commands are
effected using the popup menu (right mouse button)
Distinguishing States
States listed in a node are thus far indistinguishable. To
distinguish states in a node N (if this is possible), expand N by
creating two or more children and selecting a symbol from the
alphabet, say b. For every state in N, calculate the state
reachable from N with arc b. If all the reachable states are
currently in the same leaf node, then the states in N are thus
far still indistinguishable. If the reachable states currently
appear in different leaf nodes, then the states in N are
distinguishable and grouped into sets based on the groups of
their reachable states.
Drawing the Minimum State DFA
The second minimizing window appears with all the states
generated by the tree already placed. The only thing that needs
to be filled in are the transitions, using the original DFA as a
model. You can use the Check done, Solve, and Show options from
the menubar to check or finish the machine. They work exactly
like the ones in the NFA to DFA window. See the help on NFA to
DFA for detailed descriptions of these options.