A finite state system is a mathematical model used to describe the behavior of a system that can be in a finite number of states. It is a type of automaton that consists of a finite set of states, a set of input symbols, a set of transition functions, and a set of output functions.
A finite state system is typically represented using a finite state machine (FSM), which is a graphical representation of the system that shows the possible states, the input symbols that can cause a transition between states, and the output functions that produce a response based on the current state and input.
The behavior of a finite state system is determined by the sequence of input symbols that it receives and the transition functions that define how the system responds to those inputs. The system transitions from one state to another based on the input it receives and the rules defined by the transition functions. When the system is in a particular state, it may also produce an output based on the output functions defined for that state.
Finite state systems are used to model a wide variety of systems, including computer programs, communication protocols, and control systems. They are particularly useful for modeling systems that exhibit discrete behavior, where the system can only be in a finite number of states and the behavior of the system is determined by the sequence of inputs it receives.
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