In this paper, we define the notion of biRFSA which is a residual finate state
automaton (RFSA) whose the reverse is also an RFSA. The languages recognized by
such automata are called biRFSA languages. We prove that the canonical RFSA of a
biRFSA language is a minimal NFA for this language and that each minimal
NFA for this language is a sub-automaton of the canonical RFSA. This leads
to a characterization of the family of biRFSA languages.
In the second part of this paper, we define the family of biseparable automata.
We prove that every biseparable NFA is uniquely minimal among all NFAs recognizing
a same language, improving
the result of H. Tamm and E. Ukkonen for bideterministic automata.