Planexistenceprobleem

Planexistenceprobleem, or plan existence problem in English, is a fundamental decision problem in automated planning. It asks whether there exists a sequence of actions that, starting from a given initial state, achieves a state that satisfies the goal conditions.

A planning problem is typically defined by a set of predicates, an initial state I expressed as a conjunction of literals, a goal G expressed as a set of literals, and a finite set of actions. Each action has preconditions, add effects, and delete effects. A plan is a finite sequence of actions; applying the plan to I yields a state that satisfies G. If such a sequence exists, the problem has a plan; otherwise it does not.

In classical planning frameworks, such as STRIPS or SAS+, the existence question is closely related to plan generation: many planners aim to construct a valid plan when one exists. Practically, methods include forward or backward search, planning graphs, and encodings to SAT or SMT solvers.

Computationally, the plan existence problem for deterministic, fully observable planning is PSPACE-complete in the general case. The exact difficulty depends on the representation and constraints; restrictions (for example, limited plan length, or specific action forms) can reduce complexity, while planning under uncertainty or with nondeterministic effects raises higher complexity classes.

Planexistenceprobleem is widely used in robotics, logistics, and automated scheduling and remains a central topic in AI planning research. Related concepts include plan generation, STRIPS, PDDL, and state-space search.