Semisimple reduction conjecture for the Černý conjecture

A semisimple automaton is an automaton in the class considered in the paper for which the semisimple reduction is defined. Semisimple conjecture. If the Černý conjecture is solved for semisimple automata, then it holds in general.

The paper describes this as a more general version of its Radical Conjecture and identifies proving the Černý conjecture for semisimple automata as a route toward the general case. Its resolution is not established in the supplied text.