Question Background
A finite-state machine can be defined as a 5-tuple as follows (Sipser, pg. 35):
The image below (taken from the Wikipedia article on autamata theory) seems to suggest that combinational logics can be used to define formal grammars that describe formal languages just the same as regular expressions/FSMs, pushdown automatons, and turing machines.
The Question
Is this, in fact, the case? And if so, what is the formal definition of a combinational logic? Is it a finite automata/5-tuple that has a transition function that always specifies a transition to it's one and only state (since it is time-indepedent)? NOTE: I consider it inappropriate to couple boolean logic and digital circuitry to a mathematical model which should strive for maximal generalization.
References
Sipser, Introduction to the Theory of Computation, (2nd Edition). Thompson Course Technology, 2006.