Transition System
A transition system is a foundational concept in theoretical computer science and computational theory, providing a framework to model the behavior of discrete systems through states and transitions. It consists of a set of states representing different configurations or conditions of the system and a set of transitions that describe how the system can move from one state to another.
These transitions can be labeled with actions or events that trigger the transition between states, allowing for the representation of the system's dynamics. Transition systems are used to formalize the behavior of a wide range of computational and non-computational systems, from software programs and algorithms to complex networks and automated systems, enabling the analysis of their properties, such as reachability, safety, and liveness.
In the field of Artificial Intelligence and Machine Learning, transition systems can be used to model the environment in reinforcement learning problems, where an agent interacts with an environment to achieve a certain goal. For example, in a simple maze-solving task, each position in the maze can be represented as a state in the transition system, and the transitions could represent the agent's movements (e.g., up, down, left, right).
The labels on the transitions indicate the action taken by the agent to move from one state (position) to another. The transition system provides a structured way to represent all possible paths the agent can take to reach the goal, facilitating the application of learning algorithms to find optimal strategies.
Similarly, transition systems are used in automated planning, where the states represent different configurations of the world, and the transitions represent actions that change the world state, enabling the planning system to find sequences of actions that achieve desired outcomes.