A finite state machine (FSM), also known as finite state automation, is a computational model that can be implemented in hardware or software to model and simulate sequential logic.

This computing model is based on a hypothetical machine with one or more states. Only one single state of this machine may be operational at any given moment. The machine must change states to execute various operations according to inputs.

Finite-state automata were first developed by Von Neumann and Morgenstern’s automata theory. The Turing Machine is also a member of the family of data structures in this field.

States and transitions are the most fundamental components of a state machine. A state is a system’s condition influenced by past inputs and responds to future inputs. The first state is assigned as the initial state; this is when the machine’s execution begins. A state transition specifies which input causes one state to change to another. States, as well as transitions and outputs, are created following the state machine type.

The term machine may be misleading because computer scientists rarely simulate physical machines. Imagine a simple state machine with two states: Off and On. The initial state is On; it is activated when the state machine is run. The active state is switched from On to Off when the input button is pushed.

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**Origins of finite state machines**

There are two types of finite state machine origins in automata theory. One of them is called the Moore machine, named after its creator Edward Moore, first introduced in 1956. The structure of a Moore machine is similar to that of a Turing machine, but there are some differences. States exist in Moore machines, as well as transitions. The output is solely determined by the current state rather than any input. George H. Mealy created the other type of finite state machines, known as Mealy machines, in 1955. Unlike Moore machines, Meal machines generate outputs only on state changes, not during states.

**Basics of Automata Theory**

Automata theory is a cutting-edge field of study in computer science. In the 20th century, mathematicians began developing theoretical and physical machines that imitated human behavior, such as calculating faster and more accurately.

The word automaton, derived from “automation” and “automatic”, refers to processes that automatically execute to create specific procedures. Automata theory, in a nutshell, focuses on the logic of computation as it applies to simple machines known as automata. Computer scientists can utilize automata to understand how computers compute functions and solve issues and what it means for a function to be defined as computable or a question to be described as decidable.

A finite automaton is the simplest type of automata for calculation. It can only compute fundamental functions; therefore, it isn’t an adequate computing model. Furthermore, because a finite-state machine cannot generalize computations, it has limited power.

**Types of finite state machines**

Deterministic finite state machines, often known as deterministic finite automata, and non-deterministic finite state machines, also known as non-deterministic finite automata, are the two types of finite state machines. Although there are minor variations in how state machines are represented graphically, the concepts behind them are all derived from the same computational ideas.

Deterministic finite automata recognize or accept regular languages. A language is regular if a deterministic finite automaton accepts it. Finite state machines are generally learned using languages composed of binary strings that follow a specified structure. Binary strings can be used to create both regular and non-regular languages.

A finite-state machine (FSM) and the Turing machine are two distinct types of computers that operate entirely differently. A typical example of this distinction is as follows:

Consider the modern CPU. A machine’s bits can be in only two states (0 or 1) since they are all binary. As a result, the number of possible states is limited. Furthermore, while evaluating the components of a computer that a CPU interfaces with, there are just a finite number of potential inputs from the computer’s mouse and keyboard. The conclusion that a CPU may be modeled as a finite-state machine is supported because it acts like other machines, such as a switch and oscillator.

Now, let’s take a computer as an example. A computer has an infinite number of interactions, each of which can be in only two states (0 or 1). It’s difficult to simulate a computer within the confines of a finite-state machine. However, higher-level, infinite, and more powerful automata could accomplish this task.

**Difference between deterministic and non-deterministic finite automata**

The phrase DFA refers to a Deterministic Finite Automaton. A Finite Automata is considered deterministic if, for every input symbol, there is only one resultant state, i.e., one transition. In the case of NFA (Nondeterministic Finite Automaton), a Finite Automata is considered non-deterministic if there are multiple possible transitions from one state on the same input.

**Real-world examples of finite state machines**

Although the theoretical explanations may sound unfamiliar, we come across many examples of finite state machines every day without realizing it. For example, traffic lights change to one of the red, yellow, and green states at certain time intervals. On the other hand, safe vaults will switch from locked state to unlocked state when correct combinations are entered, while incorrect combinations will cause them to revert to the locked state.