Transition System
A formal model used to represent and analyze the dynamic behavior of systems by defining states and transitions between them based on actions or events.
Transition systems are an essential tool in AI for modeling and reasoning about the behavior of systems, especially in contexts where numerous states and possible transitions need to be managed, such as in automated planning, model checking, and formal verification. These systems are characterized by their ability to represent complex, discrete changes in a system's state due to specific actions or events, which is critically important in verifying the correctness of algorithms, ensuring safety properties, and optimizing decision-making processes. In AI, transition systems often underpin algorithms that require understanding and predicting state changes, contributing to developments in robotic control systems, game playing, and solving Markov Decision Processes (MDPs).
The term transition system has roots in theoretical computer science, traced back to the 1960s during the development of automata theory, but it gained significant traction in the realm of AI and formal methods throughout the late 1970s and 1980s as computational models became crucial in system verification and automated reasoning.
Key contributors to the development of transition systems include David Harel, who advanced their application in statecharts, a popular visual formalism for complex systems, and Amir Pnueli, whose work in temporal logic laid the groundwork for using transition systems in verifying concurrent systems. These contributions have significantly shaped how AI practitioners develop and reason about dynamic systems.