Zustandsübergangsgraph

A Zustandsübergangsgraph, translated as state transition graph, is a conceptual tool used to model the behavior of a system that can exist in a finite number of distinct states. The graph consists of nodes, which represent the states, and directed edges, which represent the transitions between these states. Each edge is typically labeled with the event or condition that triggers the transition.

These graphs are fundamental in various fields, including computer science, engineering, and linguistics, for describing and analyzing systems that change their configuration over time. For example, in software development, a state transition graph can illustrate the possible states of a user interface element, like a button, and the actions that cause it to change from one state to another (e.g., from "idle" to "hovered" to "pressed").

The concept is closely related to finite state machines (FSMs) and automata theory. A state transition graph provides a visual representation of the state space and the dynamics of an FSM. Analyzing the graph allows for understanding all possible sequences of states and identifying potential issues such as dead ends or unreachable states. Properties like reachability, cycles, and state equivalence can be determined by examining the structure of the graph. Applications include protocol design, compiler construction, and control system modeling.