  Reversible forms of computations are often interesting from an energy
efficiency point of view. When the computation device in question is an
automaton, it is known that the minimal reversible automaton recognizing a
given language is not necessarily unique, moreover, there are languages having
arbitrarily large reversible recognizers possessing no nontrivial reversible
congruence. However, the exact characterization of this class of languages was
open. In this paper we give a forbidden pattern capturing the reversible
regular languages having only finitely many reduced reversible automata,
allowing an efficient (NL) decision procedure.
