Comments on: How do you determine if a dfa is minimal

Question: How do you determine if a dfa is minimal

rdr — Sun, 20 Apr 2008 12:19:10 -0800

Is there an elegant algorithm to determine if a dfa is minimal? Obviously you can minimize a dfa and then check to see if the result is isomorphic to the original. Is there another way?

By: b1tr0t

b1tr0t — Sun, 20 Apr 2008 13:11:41 -0800

Did you try google?

By: rdr

rdr — Sun, 20 Apr 2008 13:30:43 -0800

That's not what I asked. I'm not asking how to build a minimal dfa. I'm asking if there's a way to test if a dfa is minimal.

By: zixyer

zixyer — Sun, 20 Apr 2008 14:14:59 -0800

It seems like all you have to check for is unreachable states and equivalent states. If there aren't any of either, the DFA is minimal.

You can check for equivalent states by looking at the transition function. If delta(q, a) = delta(r, a) for all a in the alphabet and two states q and r, the states are equivalent.

Unreachable states are ones that have no path from the initial state.

By: rdr

rdr — Sun, 20 Apr 2008 14:42:59 -0800

Thanks. Once I read your answer I can see how your answer is implied by how subset construction terminates.