A sufficient condition to polynomially compute a minimum separating DFA

The computation of a minimal separating automaton (MSA) for regular languages has been studied from many different points of view, from synthesis of automata or Grammatical Inference to the minimization of incompletely specified machines or Compositional Verification. In the general case, the problem is NP-complete, but this drawback does not prevent the problem from having a real application in the above-mentioned fields. In this paper, we propose a sufficient condition that guarantees that the computation of the MSA can be carried out with polynomial time complexity.