A finite automaton is a finite state machine in which certain states are identified as accepting. The language accepted by a finite automataton consists of the labels of all the paths from an initial state to an accepting state.
See: http://www.wikiwand.com/en/Deterministic_finite_automaton
In the DOT format, accepting states are denoted by a double circle, following the standard convention. For instance, the dot encoding for the Toy DFA benchmark is:
digraph g {
__start0 [label="" shape="none"]
s1 [shape="doublecircle" label="s1"]
s2 [shape="circle" label="s2"]
__start0 -> s1
s1 -> s2[label="0"]
s1 -> s1[label="1"]
s2 -> s1[label="0"]
s2 -> s2[label="1"]
}