statemachines

A state machine, sometimes written as statemachine, is a computational model used to design computer programs and sequential logic. It consists of a finite set of states, a finite set of inputs (events), a transition function that determines how states change in response to inputs, and optional actions associated with transitions or states. The machine starts in a designated initial state and produces behavior by moving between states as events occur.

There are several variants. Deterministic finite automata (DFA) have exactly one transition for each input in every state, while non-deterministic automata (NFA) may have multiple possible transitions. For output behavior, Moore machines emit outputs according to the current state, while Mealy machines emit outputs based on the state and input. Hierarchical and concurrent variants, such as statecharts, extend the basic model with nesting and parallel regions.

A common representation is a state diagram, where nodes denote states and directed edges denote transitions labeled with event names, guard conditions, and actions. Transitions can include entry and exit actions for states, and some models distinguish between internal transitions. In formal terms, a DFA or Mealy/Moore machine is described by its state set, input alphabet, transition function, and output function.

State machines are widely used in software engineering and embedded systems to model control flow, user interfaces, protocol handlers, parsers, and game logic. They support modular design, easier testing, and formal reasoning about properties such as deadlock freedom and reachability. They can be implemented as code, tables, or generated from model tools.

State machines have roots in automata theory developed in the 20th century and were popularized by Harel's Statecharts and later by UML state machine diagrams. They remain a foundational tool for modeling predictable, event-driven behavior across engineering disciplines.