It is well known that the emptiness problem for binary probabilistic automata and so
for quantum automata is undecidable. We present the current status of the emptiness problems
for unary probabilistic and quantum automata with connections with Skolem’s and positivity
problems. We also introduce the concept of linear recurrence automata in order to show the
connection naturally. Then, we also give possible generalizations of linear recurrence relations
and automata on vectors