States, Transitions and Finite-State Transition System :

Let us first give some intuitive idea about a state of a system and state transitions before describing finite automata.

Informally, a state of a system is an instantaneous description of that system which gives all relevant information necessary to determine how the system can evolve from that point on.

Transitions are changes of states that can occur spontaneously or in response to inputs to the states. Though transitions usually take time, we assume that state transitions are instantaneous (which is an abstraction).

Some examples of state transition systems are: digital systems, vending machines, etc.

A system containing only a finite number of states and transitions among them is called a finite-state transition system.

Finite-state transition systems can be modeled abstractly by a mathematical model called finite automation.