Cryptanalytical finite automaton invertibility with finite delay

The paper continues an investigation of the cryptanalytical invertibility concept with a finite delay introduced by the author for finite automata. Here, we expound an algorithmic test for an automaton $A$ to be cryptanalytically invertible with a finite delay, that is, to have a recovering function $f$ which allows to calculate a prefix of a length $m$ in an input sequence of the automaton $A$ by using its output sequence of a length $m+\tau$ and some additional information about $A$ defining a type of its invertibility and known to cryptanalysts. The test finds out whether the automaton $A$ has a recovering function $f$ or not and if it has, determines some or, may be, all of such functions. The test algorithm simulates a backtracking method for searching a possibility to transform a binary relation to a function by shortening its domain to a set corresponding to the invertibility type under consideration.