View source for Finite State Machines

==Introduction==

A [[Finite State Machine|Finite State Machine (FSM)]] is a mathematical model of computation used to design both computer programs and sequential logic circuits. It is conceived as an abstract machine that can be in one of a finite number of states. The machine is only in one state at a time; the state it is in at any given time is called the current state. It can change from one state to another when initiated by a triggering event or condition, this is called a transition.

[[Image:Detail-36601.jpg|thumb|center|A simple representation of a finite state machine.|class=only_on_mobile]]
[[Image:Detail-36602.jpg|thumb|center|A simple representation of a finite state machine.|class=only_on_desktop]]

==Definition==

A Finite State Machine is defined by a list of its states, its initial state, and the conditions for each transition. FSMs are of two types: acceptors or recognizers; and transducers. Acceptors have a boolean end state (accept or reject) and produce a binary output, they are used as control circuits. Transducers produce an output based on given inputs and are used in algorithmic applications.

==Components of a Finite State Machine==

Finite State Machines have five parts:

1. A finite set of states (Q)
2. A finite set of input symbols (Σ)
3. A finite set of output symbols (Γ)
4. A transition function (δ)
5. An initial state (q0)

==Types of Finite State Machines==

There are two types of FSMs: Mealy Machines and Moore Machines. 

===Mealy Machine===

A [[Mealy Machine]] is a FSM whose output values are determined both by its current state and the current inputs. This is in contrast to a Moore Machine, whose (Moore) output values are determined solely by its current state.

===Moore Machine===

A [[Moore Machine]] is a FSM whose output values are determined solely by its current state. This is in contrast to a Mealy Machine, whose (Mealy) output values are determined both by its current state and the current inputs.

==Applications of Finite State Machines==

FSMs have numerous applications in computer science, linguistics, artificial intelligence, systems biology, bioinformatics, and computer hardware, among others. 

===In Computer Science===

In computer science, finite state machines are widely used in modeling of application behavior, design of hardware digital systems, software engineering, compilers, network protocols, and the study of computation and languages.

===In Linguistics===

In [[Computational Linguistics]], finite state machines are used in the computational models of natural language grammars and languages.

===In Artificial Intelligence===

In artificial intelligence, finite state machines are used to model the behavior of entities such as software agents or robots, allowing a simple way to provide a "brain" for a software or robotic entity.

===In Systems Biology and Bioinformatics===

In systems biology and bioinformatics, finite state machines are used to model and simulate genetic networks and biochemical pathways.

===In Computer Hardware===

In computer hardware, finite state machines are used in the design of digital circuits for sequential logic, such as computer memory and CPUs.

==Advantages and Disadvantages of Finite State Machines==

Like any other model, finite state machines have their advantages and disadvantages.

===Advantages===

1. Simplicity: FSMs are simple and intuitive. They provide a clear, visual representation of control flow.
2. Modularity: FSMs can be easily composed with other FSMs to create more complex behavior.
3. Predictability: FSMs have a predictable and deterministic behavior.

===Disadvantages===

1. State Explosion: For complex systems, the number of states in an FSM can grow exponentially, leading to unmanageable state complexity.
2. Lack of Flexibility: FSMs are not suitable for systems where the number of states is dynamic or not known in advance.

==Conclusion==

Finite State Machines are a fundamental concept in computer science and have a wide range of applications. Despite their limitations, they are a powerful tool for modeling and understanding complex systems.

==See Also==

* [[Automata Theory]]
* [[Formal Language]]
* [[Computational Model]]

[[Category:Computer Science]]
[[Category:Mathematical Concepts]]
[[Category:Programming Concepts]]