Mooremasjiner

Mooremasjiner, commonly referred to in English as Moore machines, are a theoretical model of computation used in automata theory and digital design. They are a type of deterministic finite-state machine whose output is a function solely of the current state, not the input that led to that state.

Definition and structure: A Moore machine is defined as a 6-tuple (S, s0, Σ, Λ, δ, λ), where S is a finite set of states, s0 ∈ S is the initial state, Σ is a finite input alphabet, Λ is a finite output alphabet, δ: S × Σ → S is the state-transition function, and λ: S → Λ is the output function. The machine starts in s0 and, at each step, reads an input symbol, transitions to δ(s, a), and produces output λ(s) associated with the state before the transition. In some formulations, the initial output is λ(s0) and outputs may change only when the state changes.

Key properties: the output of a Moore machine depends only on the current state, making outputs stable between input changes. The model is deterministic if both δ and λ are fixed functions. Moore machines are often contrasted with Mealy machines, where outputs depend on both the current state and the input.

Relation to other models: any Moore machine has an equivalent Mealy machine representation, potentially with a different state count, and vice versa, though they differ in when outputs may change relative to inputs. Both are foundational in the study of finite-state systems and sequential logic.

History and applications: the model is named after Edward F. Moore, who introduced it in 1956. Moore machines are used in the design of synchronous sequential circuits, protocol modeling, and various state-based software tools, where predictable output timing is advantageous.