An Introduction to Finite Automata and their Connection to Logic

The word automaton (plural: automata) was originally used to refer to devices like clocks and watches, as well as mechanical marvels built to resemble moving humans and animals, whose internal mechanisms are hidden and which thus appear to operate spontaneously. In theoretical computer science, the finite automaton is among the simplest models of computation: A device that can be in one of finitely many states, and that receives a discrete sequence of inputs from the outside world, changing its state accordingly. This is in marked contrast to more general and powerful models of computation, such as Turing machines, in which the set of global states of the device—the so-called instantaneous descriptions—is infinite. A finite automaton is more akin to the control unit of the Turing machine (or, for that matter, the control unit of a modern computer processor), in which the present state of the unit and the input symbol under the reading head determine the next state of the unit, as well as signals to move the reading head left or right and to write a symbol on the machine’s tape. The crucial distinction is that while the Turing machine can record and consult its entire computation history, all the