I present several computational complexity results for propositional STRIPS planning, i.e., STRIPS planning restricted to ground formulas. Different planning problems can be defined by restricting the type of formulas, placing limits on the number of pre- and postconditions, by restricting negation in pre- and postconditions, and by requiring optimal plans. For these types of restrictions, I show when planning is tractable (polynomial) and intractable (NPhard) . In general, it is PSPACE-complete to determine if a given planning instance has any solutions. Extremely severe restrictions on both the operators and the formulas are required to guarantee polynomial time or even NP-completeness. For example, when only ground literals are permitted, determining plan existence is PSPACE-complete even if operators are limited to two preconditions and two postconditions. When definite Horn ground formulas are permitted, determining plan existence is PSPACE-complete even if operators are limited t...

We have previously reported a number of tractable planning problems defined in the SAS+ formalism. This report complements these results by providing a complete map over the complexity of SAS+ planning under all combinations of the previously considered restrictions. We analyze the complexity both of finding a minimal plan and of finding any plan. In contrast to other complexity surveys of planning we study not only the complexity of the decision problems but also of the generation problems. We prove that the SAS+-PUS problem is the maximal tractable problem under the restrictions we have considered if we want to generate minimal plans. If we are satisfied with any plan, then we can generalize further to the SAS+-US problem, which we prove to be the maximal tractable problem in this case.

In this paper, we examine how the complexity of domain-independent planning with STRIPS-style operators depends on the nature of the planning operators. We show

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This paper postulates a rigorous method for the construction of classical planning domain models. We describe, with the help of a non-trivial example, a tool supported method for encoding such models. The method results in an `object-centred' specification of the domain that lifts the representation from the level of the literal to the level of the object. Thus, for example, operators are defined in terms of how they change the state of objects, and planning states are defined as amalgams of the objects' states. The method features two classes of tools: for initial capture and validation of the domain model; and for operationalising the domain model (a process we call compilation) for later planning. Here we focus on compilation tools used to generate macros and goal orders to be utilised at plan generation time. We describe them in depth, and evaluate empirically their combined benefits in plan-generation speed-up. The method's main benefit is in helping the modeller to pro...

The ability of a planner to modify a plan is considered as a valuable tool for improving efficiency of planning by avoiding the repetition of the same planning effort. From a computational complexity point of view, however, it is by no means obvious that modifying a plan is computationally as easy as planning from scratch if the modification has to follow the principle of "conservatism," i.e., to reuse as much of the old plan as possible. Indeed, considering propositional STRIPS planning, it turns out that conservative plan modification is as hard as planning and can sometimes be harder than plan generation. Furthermore, this holds even if we consider modification problems where the old and the new goal specification are similar. We put these results into perspective and discuss the relationship to existing plan modification systems. 1 Introduction Plan generation in complex domains is normally a resource and time consuming process. One way to improve the efficiency of planning syste...

. In this paper we describe SINERGY, which is a highly parallelizable, linear planning system that is based on the genetic programming paradigm. Rather than reasoning about the world it is planning for, SINERGY uses artificial selection, recombination and fitness measure to generate linear plans that solve conjunctive goals. We ran SINERGY on several domains (e.g., the briefcase problem and a few variants of the robot navigation problem), and the experimental results show that our planner is capable of handling problem instances that are one to two orders of magnitude larger than the ones solved by UCPOP. In order to facilitate the search reduction and to enhance the expressive power of SINERGY, we also propose two major extensions to our planning system: a formalism for using hierarchical planning operators, and a framework for planning in dynamic environments. 1 Motivation Artificial intelligence planning is a notoriously hard problem. There are several papers [Chapman 1987, Joslin...

In this paper we describe SYNERGY, which is a general-purpose AI planning system that is based on the genetic programming paradigm. Rather than reasoning about the planning world, SYNERGY uses selection, mutation, recombination and fitness measure to generate linear plans that solve conjunctive goals. We ran SYNERGY on several domains, and the experimental results show that our planner solves problem instances that are up to two orders of magnitude larger than the ones solved by UCPOP. KEYWORDS: AI planning, genetic programming, conjunctive goals INTRODUCTION Artificial intelligence (AI) planning is known to be an extremely hard problem (see [2]), and it is generally accepted that most non-trivial planning problems are at least NPcomplete. In order to cope with the combinatorial explosion of the search problem, AI researchers proposed a wide variety of solutions, from search control rules [3] to hierarchical planning [8] to skeletal planning [5]. More recently, we witnessed the occur...

Most tractable planning problems reported in the literature have been defined by syntactical restrictions. To better exploit the inherent structure of problems, however, it is probably necessary to study also structural restrictions on the state-transition graph. We present an almost exhaustive map of complexity results for state-variable planning under all combinations of our previously analysed syntactical (P, U, B, S) and structural (I, A, O) restrictions, considering both optimal and non-optimal plan generation.

Recently several works about the computational complexity of planning appeared in the literature. In this paper we survey the main results in this area. We not only give results about the tractability /intractability of the individual problems but we also analyze sources of complexity and explain intuitively the nature of easy/hard cases. 1 Introduction Planning is the reasoning task of finding a series of actions that achieve a goal from a given initial state. One of the most important features of a Work supported by the Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo and the Progetto Speciale Pianificazione Automatica of the CNR (Italian Research Council) and by the ESPRIT Basic Research Action 6810-COMPULOG II. planning system is its efficiency, i.e. how many resources it needs in order to find a satisfactory plan. Many techniques, such as hierarchical abstraction [Sacerdoti, 1974], have been developed in order to make planning more efficient. In the same way, s...