It is true that the two DFAs may not be exactly alike. However, any two DFAs can be proved equivalent (or not) in finite time, according to this article (in PowerPoint format).

Of course, "finite" is not the same thing as "practical". The brute-force solution mentioned in that article is exponential (test all strings of length equal to the number of states). There is a second method that XORs the two DFAs that looks more promising.

It looks like either method could be adapted to test whether one DFA accepts a subset of the other.

Update: blokhead below gives the same solution in a more thoroughly-explained way.

In reply to Re^3: Comparative satisfiability of regexps. by tall_man
in thread Comparative satisfiability of regexps. by Meowse

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