, 
,
q0, F)
A deterministic finite acceptor or dfa is a quintuple:, ,
q0, F)
is a finite set of
symbols, the input alphabet,
: Q 
Q is a transition function,
Q
is the initial state,
Q is
a set of final states.
is
a function implies that every vertex has an outgoing arc for each member of .
We can also define an extended transition function 
as
:
Q
Q.
, ,
q0, F) is used as a membership criterion, then the set of strings accepted by
M is a language. That is,
:
(q0,
w) F}.
Languages that can be defined by dfas are called regular languages.