  We consider pairs of finite-length individual sequences that are realizations
of unknown, finite alphabet, stationary sources in a clas M of sources with
vanishing memory (e.g. stationary Markov sources).
  The task of a universal classifier is to decide whether the two sequences are
emerging from the same source or are emerging from two distinct sources in M,
and it has to carry this task without any prior knowledge of the two underlying
probability measures.
  Given a fidelity function and a fidelity criterion, the probability of
classification error for a given universal classifier is defined.
  Two universal classifiers are defined for pairs of $N$ -sequence: A
"classical" fixed-length (FL) universal classifier and an alternative
variable-length (VL) universal classifier.
  Following Wyner and Ziv (1996) it is demonstrated that if the length of the
individual sequences N is smaller than a cut-off value that is determined by
the properties of the class M, any universal classifier will fail with high
probability .
  It is demonstrated that for values of N larger than the cut-off rate, the
classification error relative to either one of the two classifiers tends to
zero as the length of the sequences tends to infinity.
  However, the probability of classification error that is associated with the
variable-length universal classifier is uniformly smaller (or equal) to the one
that is associated with the "classical" fixed-length universal classifier, for
any finite length.
