It is observed that using the decision algorithm for emptiness and finiteness together with closure properties we can find more decision algorithms. Here is an example.
Example : Given DFA s M1 and M2. Is L(M1) = L(M2)?
Solution : Observe that 
and 
Thus L(M1) = L(M2), iff and 
This implies that
L(M1) = L(M2) iff 
Since regular languages are closed under union, intersection and complement, we can
construct a DFA M3 recognizing the language 
If M3 accepts any string (i.e. 
) then 
) .Otherwise , L(M1) = L(M2)