Using simulation and critical points to define states in continuous search spaces

Many artificial intelligence techniques rely on the notion of a `state' as an abstraction of the actual state of the world, and an `operator' as an abstraction of the actions that take you from one state to the next. Much of the art of problem solving depends on choosing the appropriate set of states and operators. However, in realistic, and therefore dynamic and continuous search spaces, finding the right level of abstraction can be difficult. If too many states are chosen, the search space becomes intractable; if too few are chosen, important interactions between operators might be missed, making the search results meaningless. We present the idea of simulating operators using critical points as a way of dynamically defining state boundaries; new states are generated as part of the process of applying operators. Critical point simulation allows the use of standard search and planning techniques in continuous domains, as well as the incorporation of multiple agents, dynamic environments, and non-atomic variable length actions into the search algorithm. We conclude with examples of implemented systems that show how critical points are used in practice.