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 
.
