On the phenomenon of autocomputability

Following Trakhtenbrot's concept of autoreducible set, we look at the general phenomenon of autocomputability of infinite binary sequences. We define another appropriate mathematical model of this concept: the strongly autoreducible set. For this purpose, we need to introduce a natural restricted form of wtt-reduction between sets: minimal weak truth table reduction. Then we prove several basic facts about strongly autoreducible sets.