It is considered the main problem of Determinate Compact Testing (DCT): the problem of selecting of function that compresses output sequences of Tested Discrete Device (TDD). The problem of adequate probability model selection describing TDD output error is discussed and the nonhomogeneous Markov chain of arbitrary order is considered. Within this model frame the criteria of quality of realized by finite automata (FA) compressing functions is introduced. The class of asymptotical optimal FA is singled out. It is shown that probability of errors detection by belonging to this class FA tends to (M-1)/M exponentially with t, where M is number of FA states.