  Watson-Crick (WK) finite automata are working on a Watson-Crick tape, that
is, on a DNA molecule. A double stranded DNA molecule contains two strands,
each having a 5' and a 3' end, and these two strands together form the molecule
with the following properties. The strands have the same length, their 5' to 3'
directions are opposite, and in each position, the two strands have nucleotides
that are complement of each other (by the Watson-Crick complementary relation).
Consequently, WK automata have two reading heads, one for each strand. In
traditional WK automata both heads read the whole input in the same physical
direction, but in 5'->3' WK automata the heads start from the two extremes and
read the input in opposite direction. In sensing 5'->3' WK automata, the
process on the input is finished when the heads meet, and the model is capable
to accept the class of linear context-free languages. Deterministic variants
are weaker, the class named 2detLIN, a proper subclass of linear languages is
accepted by them. Recently, another specific variants, the state-deterministic
sensing 5'->3' WK automata are investigated in which the graph of the automaton
has the special property that for each node of the graph, all out edges (if
any) go to a sole node, i.e., for each state there is (at most) one state that
can be reached by a direct transition. It was shown that this concept is
somewhat orthogonal to the usual concept of determinism in case of sensing
5'->3' WK automata. In this paper a new concept, the quasi-determinism is
investigated, that is in each configuration of a computation (if it is not
finished yet), the next state is uniquely determined although the next
configuration may not be, in case various transitions are enabled at the same
time. We show that this new concept is a common generalisation of the usual
determinism and the state-determinism, i.e., the class of quasi-deterministic
sensing 5'->3' WK automata is a superclass of both of the mentioned other
classes. There are various usual restrictions on WK automata, e.g., stateless
or 1-limited variants. We also prove some hierarchy results among language
classes accepted by various subclasses of quasi-deterministic sensing 5'->3' WK
automata and also some other already known language classes.
