Automata theory is important because it allows scientists to understand how machines solve problems. An automaton is any machine that uses a specific, repeatable process to convert information into different forms. Modern computers are a common example of an automaton.
If scientists didn't study automata theory, they would have a much more difficult time designing systems that could perform repeatable actions based on specific inputs and outputs. Scientists are able to design systems that can perform specific tasks, such as personal computer systems, automatic aircraft pilots and many more, by using automata theory.
There are a number of other examples of automatons. These range from basic devices, such as a pendulum clock, to missile guidance systems and complex telephone networks.
Thermostats are a familiar example of an automaton. A thermostat checks the temperature of its surrounding environment at specific intervals, and then turns on when the temperature reaches a certain level. In this case, there are only two potential states for the thermostat: on or off.
Automatons can be much more complex than a thermostat. Modern computers have a large number of data inputs and potential states. Automata theory is used to design computers that respond to inputs by producing reliable outputs.