# Finite state machine

A finite state machine (FSM) or finite state automaton, finite automaton, or simply a state machine, 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 in only 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. An FSM is defined by a list of its states, its initial state, and the triggering condition for each transition.

FSMs are of two types: deterministic finite state machines and nondeterministic finite state machines. A deterministic finite state machine has a unique next state for each present state and input; an input of a given present state always leads to the same next state. A nondeterministic finite state machine, on the other hand, may have multiple next states for some present states and inputs. Which next state is entered depends on the implementation, not on the input.

### Accordingly, what is finite state machine with example?

A finite state machine (FSM) is a mathematical model of computation used to design algorithms or programs. It is an abstract machine that can be in one of a finite number of states. The machine is in only 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 triggered by some input; the change from one state to another is called a transition. An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition.

Here is a simple example of an FSM:

States: {s1, s2}

Initial state: s1

Inputs: a

Transitions:

s1 → s2 on input a You can also ask is a cpu a finite state machine? Yes, a CPU is a finite state machine. It has a limited number of states that it can be in, and it can only transition from one state to another in a finite amount of time. You can also ask why are finite state machines important? Finite state machines are important because they provide a way to model complex systems in a way that is easy to understand and reason about. By breaking down a complex system into a series of states and transitions between those states, we can more easily see how the system behaves and identify potential problems. Additionally, finite state machines can be used to create efficient algorithms for solving problems.

##### Moreover, what are the elements of fsm?

There are four main elements of a finite state machine: states, transitions, inputs, and outputs.

States are the different conditions that the machine can be in. Transitions are the changes of state that occur in response to inputs. Inputs are the stimuli that the machine responds to. Outputs are the results of the machine's actions. Accordingly, does fsm have memory? Yes, FSM has memory. Memory is required for keeping track of the current state of the machine as well as for storing the data required for the execution of the machine's program.