Moore machine

In the theory of computation, a Moore machine is a finite state automaton where the outputs are determined by the current state alone (and not on the input). The state diagram for a Moore machine will include an output signal for each state. Compare with a Mealy machine, which maps transitions in the machine to outputs.

The name Moore machine comes from that of their promoter: E. F. Moore, a state machine pioneer, who wrote Gedanken-experiments on Sequential Machines, pp 129 – 153, Automata Studies, Annals of Mathematical Studies, no. 34, Princeton University Press, Princeton, N. J., 1956

Most electronics are designed as clocked sequential systems. Clocked sequential systems are a restricted form of Moore machine where the state changes only when the global clock signal changes. Typically the current state is stored in flip-flops, and global clock signal is connected to the "clock" input of the flip-flops. Clocked sequential systems are one way to solve metastability problems.

Formal definition

A Moore machine can be defined as a 7-tuple { Q, Σ, Δ, δ, λ, <math>q_0<math>, F } consisting of

• a finite set of states ( Q )
• a finite set called the input alphabet ( Σ )
• a finite set called the output alphabet ( Δ )
• a transition function (δ : Q x Σ → Q ) mapping a state and an input to the next state
• an output function ( λ : Q → Δ ) mapping each state to the output alphabet.
• a start state <math>( q_0 )<math>
• a set of finish states F

The number of states in a Moore machine will be greater than or equal to the number of states in the corresponding Mealy machine.