Foundations of asymptotical theory of Determinate Compact Testing

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. Description of the class of asymptotical optimal FA is also given in terms of permutation groups and it is shown that, in general, this class places strictly “between” the transitive and primitive groupe. Class of asymptotical optimal FA realizing Checksums to Modulo M is singled out. Class of asymptotical optimal signature analyzers defined over field GF(Z) is singled out. The simple sufficient conditions describing the class of asymptotical optimal signature analyzers defined over field GF(k) (k is a prime number) are also given here.