What is the connection between combinatorial circuits and finite state automata?

Question

The diagram on the Wikipedia page of FSA shows the hierarchy of the computational devices, in that diagram it is denoted that the finite state machines are superior to the combinatorial circuits.

Combinatorial circuits are the model of propositional logic i.e. both are equivalent, where we do a discussion about the truth values of variables and the logical connectives. Whereas the models beyond the FSA process the strings and decides the membership of a string with for some language.

If there is some connection between these two models then there must be some relation between propositional logic and regular/context-free/recursive languages.

How can we construct a corresponding FSA for a given combinatorial circuit?