  In this paper we define a notion of automatic randomness tests (ART) which
capture measure theoretic typicalness of infinite binary sequences within the
framework of automata theory. An individual ART is found to be equivalent to a
deterministic B\"{u}chi automaton recognizing $\omega$-language of (Lebesgue)
measure zero. A collection of ART's induce a notion of automatic random
sequence. We provide a purely combinatorial characterization of an automatic
random sequence in the form of a disjunctive property for sequences. At last,
we compare two kinds of automatic randomness tests presented in this paper.
