Mealy machine

In the theory of computation, a Mealy machine is a finite-state machine whose output values are determined both by its current state and the current inputs. This is in contrast to a Moore machine, whose output values are determined solely by its current state. A Mealy machine is a deterministic finite-state transducer: for each state and input, at most one transition is possible. The Mealy machine is named after George H. Mealy, who presented the concept in a 1955 paper, "A Method for Synthesizing Sequential Circuits". A Mealy machine is a 6-tuple consisting of the following: a finite set of states a start state (also called initial state) which is an element of a finite set called the input alphabet a finite set called the output alphabet a transition function mapping pairs of a state and an input symbol to the corresponding next state. an output function mapping pairs of a state and an input symbol to the corresponding output symbol. In some formulations, the transition and output functions are coalesced into a single function . Mealy machines tend to have fewer states: Different outputs on arcs (n2) rather than states (n). Moore machines are safer to use: Outputs change at the clock edge (always one cycle later). In Mealy machines, input change can cause output change as soon as logic is done—a big problem when two machines are interconnected – asynchronous feedback may occur if one isn't careful. Mealy machines react faster to inputs: React in the same cycle—they don't need to wait for the clock. In Moore machines, more logic may be necessary to decode state into outputs—more gate delays after clock edge. The state diagram for a Mealy machine associates an output value with each transition edge, in contrast to the state diagram for a Moore machine, which associates an output value with each state. When the input and output alphabet are both Σ, one can also associate to a Mealy automata a Helix directed graph (S × Σ, (x, i) → (T(x, i), G(x, i))).