If the languages and even in the form of DEA before, it can be the equivalent problem also decide by both DEA in each case the minimum machine forms and then this on isomorphism checked. If this is the case, the two languages and are also equivalent.
Marco Almeida, Nelma Moreira and Rogério Reis: Testing the Equivalence of Regular Languages . In: 11th International Workshop on Descriptional Complexity of Formal Systems (DCFS 2009) EPTCS 3 . 2009, p.47-57 , doi : 10.4204 / EPTCS.3.4 , arxiv : 0907.5058 .