MealyMaschinen

MealyMaschinen is the German-language term often used to refer to Mealy machines, a class of finite-state transducers in automata theory. Named after George H. Mealy, who described the model in 1955, Mealy machines produce outputs that depend on both the current state and the current input, typically modeled as a deterministic tuple of states, input alphabet, output alphabet, transition function and output function.

Formally, a Mealy machine can be described by (S, Σ, Λ, δ, ω, s0) where S is a finite set of states, Σ an input alphabet, Λ an output alphabet, δ: S × Σ → S is the state transition function, ω: S × Σ → Λ is the output function, and s0 is the initial state. This contrasts with Moore machines, whose outputs depend only on state; Mealy machines often achieve equivalent behavior with fewer states by emitting outputs on transitions.

MealyMaschinen are widely used in digital circuit design, protocol and control-system modeling, lexical analysis, and embedded-system state controllers. Their properties support formal verification techniques such as equivalence checking and minimization, and they are amenable to implementation in hardware description languages and as software-state machines.

Practical considerations include the timing and synchronization of outputs with inputs in hardware implementations, and systematic conversion to and from Moore representations when required by tooling or design constraints. The concept remains fundamental in theoretical computer science and engineering education.