Zustandmaschine

A Zustandmaschine, often translated as state machine or finite automaton, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of states at any given time. The machine can change from one state to another when triggered by some external inputs; the change from one state to another is called a transition. An input sequence is processed by the machine, and the sequence of states it goes through is determined by the transitions.

The concept of a Zustandmaschine is fundamental in computer science and has wide-ranging applications. It is used in the design of digital circuits, compilers, network protocols, and artificial intelligence. In software development, Zustandmaschinen are often implemented to manage complex behaviors, control flows, and represent different stages of a process. For example, a user interface element might have states like "idle," "hover," and "clicked," with transitions triggered by user interaction.

Formally, a Zustandmaschine can be defined as a tuple consisting of a set of states, an alphabet of input symbols, a transition function, a start state, and a set of accept states. The transition function dictates the next state based on the current state and the input symbol. The start state is the initial state of the machine, and the accept states are those that indicate successful completion of a computation or recognition of a pattern. Despite their simplicity, Zustandmaschinen are capable of recognizing a wide range of languages, known as regular languages.