The power of real-time Turing machines using sublinear space is investigated.
In contrast to a claim appearing in the literature, such machines can accept
non-regular languages, even if working in deterministic mode. While maintaining
a standard binary counter appears to be impossible in real-time, we present a
guess and check approach that yields a binary representation of the input
length. Based on this technique, we show that unary encodings of languages
accepted in exponential time can be recognized by nondeterministic real-time
Turing machines