Automata Theory
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 
.
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