Plan Existence Problem Research Articles

On the Computational Complexity of Plan Verification, (Bounded) Plan-Optimality Verification, and Bounded Plan Existence

In this paper we study the computational complexity of several reasoning tasks centered around the bounded plan existence problem. We do this for standard classical planning and hierarchical task network (HTN) planning and each for a grounded and a lifted representation. Whereas bounded plan existence complexity is known for classical planning, it has not yet been studied for HTN planning. For plan verification, results were available for both formalisms except for the lifted HTN planning. We will present lower and upper bounds of the complexity of plan verification in lifted HTN planning and provide novel insights into its grounded counterpart, in which we show that verification is not just NP-complete in the general case, but already for a severely restricted special case. Finally, we show the complexity concerning verifying the optimality of a given plan and discuss its connection to the bounded plan existence problem.

Assessing the Expressivity of Planning Formalisms through the Comparison to Formal Languages

From a theoretical perspective, judging the expressivity of planning formalisms helps to understand the relationship of different representations and to infer theoretical properties. From a practical point of view, it is important to be able to choose the best formalism for a problem at hand, or to ponder the consequences of introducing new representation features. Most work on the expressivity is based either on compilation approaches, or on the computational complexity of the plan existence problem. Recently, we introduced a new notion of expressivity. It is based on comparing the structural complexity of the set of solutions to a planning problem by interpreting the set as a formal language and classifying it with respect to the Chomsky hierarchy. This is a more direct measure than the plan existence problem and enables also the comparison of formalisms that can not be compiled into each other. While existing work on that last approach focused on different hierarchical problem classes, this paper investigates STRIPS with and without conditional effects; though we also tighten some existing results on hierarchical formalisms. Our second contribution is a discussion on the language-based expressivity measure with respect to the other approaches.

Oversubscription Planning: Complexity and Compilability

Many real-world planning problems are oversubscription problems where all goals are not simultaneously achievable and the planner needs to find a feasible subset. We present complexity results for the so-called partial satisfaction and net benefit problems under various restrictions; this extends previous work by van den Briel et al. Our results reveal strong connections between these problems and with classical planning. We also present a method for efficiently compiling oversubscription problems into the ordinary plan existence problem; this can be viewed as a continuation of earlier work by Keyder & Geffner.

Tractable plan existence does not imply tractable plan generation

We present a class, 3S, of planning instances such that the plan existence problem is tractable while plan generation is provably intractable for instances of this class. The class is defined by simple structural restrictions, all of them testable in polynomialdtime. Furthermore, we show that plan generation can be carried out in time bounded by a polynomial in the size of the input and the size of the generated solution. For this class, we propose a provably sound and complete incremental planner, i.e., a planner that can usually output an executable prefix of the final plan before it has generated the whole plan.

The Plan Existence Problem for a Discrete Event System

This paper proposes the usage of some relational theory concepts to solve the action planning problem in the production systems based on actions in the state space. A problem regarding the action planning was formulated here : to verify the existence of an action plan between the initial state x0 and the final state xf of a given system [S, T, x0, xf] before its effective construction. The problem solution may be obtained determining the system equivalence classes and verifying whether the states x0 and xf belong to these classes.