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Definition

# finite state machine

Finite state machine (FSM) is a term used by programmers, mathematicians, engineers and other professionals to describe a mathematical model for any system that has a limited number of conditional states of being. A practical example of a finite state machine is a set of buttons on a video game controller that are connected to a specific set of actions within the game. When a user inputs hitting certain buttons, the system knows to implement the actions that correspond.

The makeup of a finite state machine consists of the following:

• A set of potential input events.
• A set of probable output events that correspond to the potential input events.
• A set of expected states the system can exhibit.

A finite state machine may be implemented through software or hardware to simplify a complex problem. Within an FSM, all states in consideration exist in a finite list and the abstract machine can only take on one of those states at a time. This approach allows each input and output scenario to be studied and tested.

An FSM may be something very abstract, like a model for a business represented by an illustration, or it may be something concrete, like a vending machine or computer. The list of possible combinations of these elements is limited within a finite state machine. Alternatively, a state machine can be fuzzy. A fuzzy state machine allows the possibility of points of data that are not within discrete, pre-designated categories.

## Automata theory

While the word machine traditionally includes a physical component, in this context it refers to an abstraction that could take the form of anything from a set of input events, to a computer, simple analog machine or theoretical model of an abstract concept in automata theory. Automata is a theoretical branch of computer science and discrete mathematics that focuses on the logic of simple machines. The types of computational models within automata theory include:

• Finite state machines—Models for any system with a limited number of conditional states of being.
• Pushdown automata – More complicated than finite state machines, these use regions of memory called stacks to store information as part of a model.
• Linear-bounded automata (LBA) – Similar to a Turing machine, but the data is limited to a portion of input within a finite group of inputs.
• Turing machines—The most complex mathematical model within automata theory for testing different input combinations to analyze a larger system or problem.

## State transition

When a finite state machine switches between states, it is called a state transition. Testing the quality of a system includes checking each state and state transition by considering all of the potential inputs that might be entered. In some cases, the finite state machine is set up using a programming language, and state transition functions are executed. In addition, artificial intelligence can be used to collect data about systems with pattern recognition and automated models.

For simpler problems, the same information can be displayed in tables, matrices, illustrations and flow charts, but finite state machines allow researchers to model larger and more complicated scenarios. Finite state machine diagrams show the flow of logic between input and output combinations that may appear within a specific machine.

This was last updated in September 2019

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