The mathematical study of abstract computing machines (especially Turing machines) and the analysis of algorithms used by such machines.
A connection between automata theory and number theory was provided by Christol et al. (1980), who showed that a sequence is generated by a
-automaton iff the formal
power series with coefficients
is algebraic on the field of rational elements
, where
and
are polynomials with coefficients in the finite
field
.