Zustandsübergangssystemen

Zustandsübergangssystemen, also known as state transition systems, are a mathematical and computational model used to describe the behavior of systems that can exist in a finite number of states. At any given time, a system is in one specific state. The system can transition from one state to another in response to certain events or inputs. These transitions are typically deterministic, meaning that for a given state and input, there is only one possible next state. However, non-deterministic state transition systems also exist, where multiple transitions are possible from a single state for the same input.

The formal definition of a state transition system typically includes a set of states, an initial state, and a set of transitions. Each transition specifies a current state, an input or event, and a next state. These systems are widely used in computer science for modeling the behavior of software and hardware, in control theory for designing and analyzing control systems, and in linguistics for representing grammatical structures. Examples include simple traffic light controllers, vending machines, and finite automata. The analysis of state transition systems often involves exploring reachable states, identifying cycles, and verifying properties such as liveness and safety.