How do states, inputs, outputs, and operating rules describe an automaton?

In automata theory, an automaton is defined as a logically constructed entity that converts information from one form into another according to a definite procedure. Abstractly, it is described by four fundamental components:12

• States: These represent the internal conditions of the automaton at any given moment. In many models, the automaton exists in one of a finite set of discrete states.12
• Inputs: These are external conditions or data provided to the machine, such as symbols on a tape or signals from an operator, which can influence the transition between states.12
• Outputs: These are the results produced by the automaton based on its internal processing. While some automata, known as transducers, generate outputs, others called acceptors simply recognize or "accept" specific input sequences by reaching a designated final state.13
• Operating Rules: These are the logical procedures that dictate how the automaton functions. They determine how the machine transitions from one state to the next and how it processes inputs to produce outputs or reach a final state.124

Together, these elements allow automata to be studied as mathematical systems, independent of their physical components.2