These objects are formally defined by specifying a finite alphabet, a set of states, and a transition function between those states.
One method of generating one of these constructs is to use Thompson's Construction to create an intermediate structure, then construct the power set of those states. Every "intrinsic," or "minimal" one of these structures has an associated syntactic monoid, and these constructs are classified as either Moore or Mealy types depending on what sort of function gives their output. The Knuth-Morris-Pratt algorithm generates one of these constructs, which it uses to perform a string search. A set of symbols that brings one of these to an accepting state is said to belong to its language, and it is impossible to construct one of these objects, which does not accept a regular language as a consequence of the Pumping Lemma. These objects are formally defined by specifying a finite alphabet, a set of states, and a transition function between those states. For 10 points, name this theoretical construct, often used to model simple aspects of computing.
One method of generating one of these constructs is to use Thompson's Construction to create an intermediate structure, then construct the power set of those states.
Deterministic Finite Automata [accept Deterministic Finite-state Machines, prompt on just Finite-state Machine or Finite Automata. Technically, I guess you should prompt on push-down automata, linearly bounded automata, and Turing machines, since a DFA is a special case of each, but that might be going a bit far]