Results 1  10
of
157
The Computational Complexity of Propositional STRIPS Planning
 Artificial Intelligence
, 1994
"... 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 ..."
Abstract

Cited by 363 (3 self)
 Add to MetaCart
(Show Context)
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 PSPACEcomplete 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 NPcompleteness. For example, when only ground literals are permitted, determining plan existence is PSPACEcomplete even if operators are limited to two preconditions and two postconditions. When definite Horn ground formulas are permitted, determining plan existence is PSPACEcomplete even if operators are limited t...
HTN planning: Complexity and expressivity
 In AAAI94
, 1994
"... Most practical work on AI planning systems during the last fteen years has been based on hierarchical task network (HTN) decomposition, but until now, there has been very little analytical work on the properties of HTN planners. This paper describes how the complexity of HTN planning varies with var ..."
Abstract

Cited by 315 (19 self)
 Add to MetaCart
(Show Context)
Most practical work on AI planning systems during the last fteen years has been based on hierarchical task network (HTN) decomposition, but until now, there has been very little analytical work on the properties of HTN planners. This paper describes how the complexity of HTN planning varies with various conditions on the task networks.
Bridging the gap between planning and scheduling
 KNOWLEDGE ENGINEERING REVIEW
, 2000
"... Planning research in Artificial Intelligence (AI) has often focused on problems where there are cascading levels of action choice and complex interactions between actions. In contrast, Scheduling research has focused on much larger problems where there is little action choice, but the resulting orde ..."
Abstract

Cited by 118 (12 self)
 Add to MetaCart
(Show Context)
Planning research in Artificial Intelligence (AI) has often focused on problems where there are cascading levels of action choice and complex interactions between actions. In contrast, Scheduling research has focused on much larger problems where there is little action choice, but the resulting ordering problem is hard. In this paper, we give an overview of AI planning and scheduling techniques, focusing on their similarities, differences, and limitations. We also argue that many difficult practical problems lie somewhere between planning and scheduling, and that neither area has the right set of tools for solving these vexing problems.
The Computational Complexity of Probabilistic Planning
 Journal of Artificial Intelligence Research
, 1998
"... We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought; we examine totally ordered plans, acyclic plans, and loopin ..."
Abstract

Cited by 94 (6 self)
 Add to MetaCart
We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought; we examine totally ordered plans, acyclic plans, and looping plans, and partially ordered plans under three natural definitions of plan value. We show that problems of interest are complete for a variety of complexity classes: PL, P, NP, coNP, PP, NP PP, coNP PP , and PSPACE. In the process of proving that certain planning problems are complete for NP PP , we introduce a new basic NP PP complete problem, EMajsat, which generalizes the standard Boolean satisfiability problem to computations involving probabilistic quantities; our results suggest that the development of good heuristics for EMajsat could be important for the creation of efficient algorithms for a wide variety of problems.
On the Complexity of BlocksWorld Planning
 Artificial Intelligence
, 1992
"... In this paper, we show that in the bestknown version of the blocks world (and several related versions), planning is difficult, in the sense that finding an optimal plan is NPhard. However, the NPhardness is not due to deletedcondition interactions, but instead due to a situation which we call a ..."
Abstract

Cited by 92 (15 self)
 Add to MetaCart
In this paper, we show that in the bestknown version of the blocks world (and several related versions), planning is difficult, in the sense that finding an optimal plan is NPhard. However, the NPhardness is not due to deletedcondition interactions, but instead due to a situation which we call a deadlock. For problems that do not contain deadlocks, there is a simple hillclimbing strategy that can easily find an optimal plan, regardless of whether or not the problem contains any deletedcondition interactions. The above result is rather surprising, since one of the primary roles of the blocks world in the planning literature has been to provide examples of deletedcondition interactions such as creative destruction and Sussman's anomaly. However, we can explain why deadlocks are hard to handle in terms of a domainindependent goal interaction which we call an enablingcondition interaction, in which an action invoked to achieve one goal has a sideeffect of making it easier to achi...
Using RegressionMatch Graphs to Control Search in Planning
 Artificial Intelligence
, 1999
"... Classical planning is the problem of finding a sequence of actions to achieve a goal given an exact characterization of a domain. An algorithm to solve this problem is presented, which searches a space of plan prefixes, trying to extend one of them to a complete sequence of actions. It is guided by ..."
Abstract

Cited by 77 (3 self)
 Add to MetaCart
(Show Context)
Classical planning is the problem of finding a sequence of actions to achieve a goal given an exact characterization of a domain. An algorithm to solve this problem is presented, which searches a space of plan prefixes, trying to extend one of them to a complete sequence of actions. It is guided by a heuristic estimator based on regressionmatch graphs, which attempt to characterize the entire subgoal structure of the remaining part of the problem. These graphs simplify the structure by neglecting goal interactions and by assuming that variables in goal conjunctions should be bound in such a way as to make as many conjuncts as possible true without further work. In some domains, these approximations work very well, and experiments show that many classicalplanning problems can solved with very little search. 1 Definition of the Problem The classical planning problem is to generate a sequence of actions that make a given proposition true, in a domain in which there is perfect informati...
Computational Complexity of Planning and Approximate Planning in the Presence of Incompleteness
, 1999
"... In the last several years, there have been several studies about the computational complexity of classical planning assuming that the planner has complete knowledge about the initial situation. Recently, there have been proposals to use `sensing' actions to plan in the presence of incomplete ..."
Abstract

Cited by 69 (7 self)
 Add to MetaCart
In the last several years, there have been several studies about the computational complexity of classical planning assuming that the planner has complete knowledge about the initial situation. Recently, there have been proposals to use `sensing' actions to plan in the presence of incompleteness. In this paper we study the complexity of planning in such cases. In our study we use the action description language A proposed in 1991 by Gelfond and Lifschitz, and its extensions. It is known that if we consider only plans of tractable (polynomial) duration, planning in A  with complete information about the initial situation  is NPcomplete: even checking whether a given objective is attainable from a given initial state is NPcomplete. In this paper, we show that the planning problem in the presence of incompleteness is indeed harder: it belongs to the next level of the complexity hierarchy (in precise terms, it is \Sigma 2 Pcomplete). To overcome the complexity of this pro...
Concise finitedomain representations for PDDL planning tasks
, 2009
"... We introduce an efficient method for translating planning tasks specified in the standard PDDL formalism into a concise grounded representation that uses finitedomain state variables instead of the straightforward propositional encoding. Translation is performed in four stages. Firstly, we transfo ..."
Abstract

Cited by 63 (13 self)
 Add to MetaCart
(Show Context)
We introduce an efficient method for translating planning tasks specified in the standard PDDL formalism into a concise grounded representation that uses finitedomain state variables instead of the straightforward propositional encoding. Translation is performed in four stages. Firstly, we transform the input task into an equivalent normal form expressed in a restricted fragment of PDDL. Secondly, we synthesize invariants of the planning task that identify groups of mutually exclusive propositions which can be represented by a single finitedomain variable. Thirdly, we perform an efficient relaxed reachability analysis using logic programming techniques to obtain a grounded representation of the input. Finally, we combine the results of the third and fourth stage to generate the final grounded finitedomain representation. The presented approach has originally been implemented as part of the Fast Downward planning system for the 4th International Planning Competition (IPC4). Since then, it has been used in a number of other contexts with considerable success, and the use of concise finitedomain representations has become a common feature of stateoftheart planners.
Planning by Rewriting: Efficiently Generating HighQuality Plans
 In Proceedings of the Fourteenth National Conference on Artificial Intelligence
, 1997
"... Domainindependent planning is a hard combinatorial problem. Taking into account plan quality makes the task even more difficult. We introduce a new paradigm for efficient highquality planning that exploits plan rewriting rules and efficient local search techniques to transform an easytogenerate, ..."
Abstract

Cited by 60 (12 self)
 Add to MetaCart
Domainindependent planning is a hard combinatorial problem. Taking into account plan quality makes the task even more difficult. We introduce a new paradigm for efficient highquality planning that exploits plan rewriting rules and efficient local search techniques to transform an easytogenerate, but possibly suboptimal, initial plan into a lowcost plan. In addition to addressing the issues of efficiency and quality, this framework yields a new anytime planning algorithm. We have implemented this planner and applied it to several existing domains. The results show that this approach provides significant savings in planning effort while generating highquality plans. Introduction Planning is the process of generating a network of actions that achieves a desired goal from an initial state of the world. Domain independent planning accepts as input, not only the initial state and the goal, but also the domain specification (i.e., the operators). This is a problem of considerable prac...
Structure and Complexity in Planning with Unary Operators
 Journal of Artificial Intelligence Research
, 2003
"... Unary operator domains  i.e., domains in which operators have a single effect  arise naturally in many control problems. In its most general form, the problem of strips planning in unary operator domains is known to be as hard as the general strips planning problem  both are pspacecomplete. H ..."
Abstract

Cited by 53 (10 self)
 Add to MetaCart
Unary operator domains  i.e., domains in which operators have a single effect  arise naturally in many control problems. In its most general form, the problem of strips planning in unary operator domains is known to be as hard as the general strips planning problem  both are pspacecomplete. However, unary operator domains induce a natural structure, called the domain's causal graph. This graph relates between the preconditions and effect of each domain operator. Causal graphs were exploited by Williams and Nayak in order to analyze plan generation for one of the controllers in NASA's DeepSpace One spacecraft. There, they utilized the fact that when this graph is acyclic, a serialization ordering over any subgoal can be obtained quickly. In this paper we conduct a comprehensive study of the relationship between the structure of a domain's causal graph and the complexity of planning in this domain. On the positive side, we show that a nontrivial polynomial time plan generation algorithm exists for domains whose causal graph induces a polytree with a constant bound on its node indegree. On the negative side, we show that even plan existence is hard when the graph is a directedpath singly connected DAG.