## Complexity, Decidability and Undecidability Results for Domain-Independent Planning (1995)

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Venue: | ARTIFICIAL INTELLIGENCE |

Citations: | 132 - 25 self |

### BibTeX

@ARTICLE{Erol95complexity,decidability,

author = {Kutluhan Erol and Dana S. Nau and V. S. Subrahmanian},

title = {Complexity, Decidability and Undecidability Results for Domain-Independent Planning},

journal = {ARTIFICIAL INTELLIGENCE},

year = {1995},

volume = {76},

pages = {75--88}

}

### Years of Citing Articles

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### Abstract

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

### Citations

10922 | Computers and Intractability: A Guide to the Theory of NP-Completeness - Garey, Johnson - 1979 |

2438 |
The Design and Analysis of Computer Algorithms
- Aho, Hopcroft, et al.
- 1974
(Show Context)
Citation Context ...whether there is a plan of length k or less, but finding the shortest plan. This problem is at least as difficult as plan length, and in some cases harder. For example, in the Towers of Hanoi problem =-=[1]-=- and certain generalizations of it [15], the length of the shortest plan can be found in low-order polynomial time— but actually producing this plan requires exponential time and space, since the plan... |

1740 |
STRIPS: A New Approach to the Application of Theorem Proving to Problem Solving
- Fikes, Nilsson
- 1971
(Show Context)
Citation Context ... see [10]. 2 Preliminaries Researchers in planning have long been interested in planning with STRIPSstyle operators, and this interest still continues [3,5,16,22,20]. In the original 3STRIPS planner =-=[13]-=-, the planning operators’ precondition lists, add lists, and delete lists were allowed to contain arbitrary well-formed formulas in firstorder logic. However, there were a number of problems with this... |

623 |
Planning for Conjunctive Goals
- Chapman
- 1990
(Show Context)
Citation Context ...style operators depends on the nature of the planning operators. We show conditions under which planning is decidable and undecidable. Our results on this topic solve an open problem posed by Chapman =-=[5]-=-, and clear up some difficulties with his undecidability theorems. For those cases where planning is decidable, we explain how the time complexity varies depending on a wide variety of conditions: • w... |

508 |
Concrete Mathematics: A Foundation for Computer Science
- Graham, Knuth, et al.
- 1990
(Show Context)
Citation Context ... less, but finding the shortest plan. This problem is at least as difficult as plan length, and in some cases harder. For example, in the Towers of Hanoi problem [1] and certain generalizations of it =-=[15]-=-, the length of the shortest plan can be found in low-order polynomial time— but actually producing this plan requires exponential time and space, since the plan has exponential length. The definition... |

440 |
Planning in a hierarchy of abstraction spaces
- Sacerdoti
- 1974
(Show Context)
Citation Context ...nd IRI-9109755.1 Introduction Much planning research has been motivated, in one way or another, by the difficulty of producing complete and correct plans. For example, techniques such as abstraction =-=[27,6,24,31]-=- and task reduction [28,6,31] were developed in an effort to make planning more efficient, and concepts such as deleted-condition interactions were developed to describe situations which make planning... |

384 | Systematic Nonlinear Planning - Mcallester, Rosenblitt - 1991 |

377 |
Generating Project Networks
- Tate
- 1977
(Show Context)
Citation Context ...ally ordered set of actions P , the question is whether a is necessarily/possibly true after execution of P . This question is especially important in partial-order planners such as NOAH [28], NONLIN =-=[32]-=-, and SIPE [33]. For example, McDermott [21] says “unfortunately, partial orders have a big problem, that there is no way of deciding what is true for sure before a step without considering all possib... |

251 | Introduction to Artificial Intelligence - Charniak, McDermott - 1985 |

216 |
Mathematical Logic
- Shoenfield
- 1967
(Show Context)
Citation Context ...nd atoms are currently true: if a ground atom A is in state S, then A is true in state S, and if B /∈ S, then B is false in state S. Thus, a state is simply an Herbrand interpretation (cf. Shoenfield =-=[29]-=-) for the language L, and hence each formula of first-order logic is either satisfied or not satisfied in S according to the usual first-order logic definition of satisfaction. We use STRIPS-style pla... |

213 |
The non-linear nature of plans
- Sacerdoti
- 1975
(Show Context)
Citation Context ...uch planning research has been motivated, in one way or another, by the difficulty of producing complete and correct plans. For example, techniques such as abstraction [27,6,24,31] and task reduction =-=[28,6,31]-=- were developed in an effort to make planning more efficient, and concepts such as deleted-condition interactions were developed to describe situations which make planning difficult. Despite the ackno... |

210 | Conditional nonlinear planning
- Peot, Smith
- 1992
(Show Context)
Citation Context ...nts. Our results show that even with a number of additional restrictions, planning is still undecidable. We also correct a misimpression about this theorem, which has been thought by some researchers =-=[26,11]-=- to refer to operators that have conditional effects. It does not—and our decidability and complexity results are unaffected by whether or not the operators have conditional effects. (5) Chapman [5] a... |

201 |
Planning as Search: A Quantitative Approach
- Korf
- 1987
(Show Context)
Citation Context ...forms in exponential time. It is not very easy to compare our results with theirs, because we use a different formalism, but we can safely state that we analyze a much broader range of problems. Korf =-=[18]-=- has pointed out that given certain assumptions, one can reduce exponentially the time required to solve a conjoined-goal planning problem, provided that the individual goals are independent. Yang, Na... |

135 | Domain-independent Planning: Representation and Plan Generation
- Wilkins
- 1984
(Show Context)
Citation Context ...t of actions P , the question is whether a is necessarily/possibly true after execution of P . This question is especially important in partial-order planners such as NOAH [28], NONLIN [32], and SIPE =-=[33]-=-. For example, McDermott [21] says “unfortunately, partial orders have a big problem, that there is no way of deciding what is true for sure before a step without considering all possible step sequenc... |

128 | On the semantics of STRIPS
- Lifschitz
- 1987
(Show Context)
Citation Context ...owed to contain arbitrary well-formed formulas in firstorder logic. However, there were a number of problems with this formulation, such as the difficulty of providing a well-defined semantics for it =-=[19]-=-. Thus, in subsequent work, researchers have placed some restrictions on the nature of the planning operators [24]. Typically, the precondition lists, add lists and delete lists contain only atoms, an... |

119 | Complexity results for planning - Bylander - 1991 |

95 |
Synthesizing plans that contain actions with context-dependent effects
- Pednault
- 1988
(Show Context)
Citation Context ...ielded some surprising results. For example, Gupta and Nau [16,17] have shown that contrary to prior expectations, deleted-condition interactions are easy to handle in blocks-world planning. Pednault =-=[25]-=- suggests that since planning is intractable in general, researchers should try to identify constraints that will lead to efficient planning. The current paper addresses this goal, by examining how th... |

79 |
Reasoning about partially ordered events
- Dean, Boddy
- 1988
(Show Context)
Citation Context ...tors that have conditional effects. It does not—and our decidability and complexity results are unaffected by whether or not the operators have conditional effects. (5) Chapman [5] and Dean and Boddy =-=[8]-=- studied planning with conditional operators, and showed that the problem of deciding whether a proposition is necessarily true after a partially ordered plan (a.k.a modal truth criterion) is NP-hard ... |

79 | On the complexity of blocks-world planning
- Gupta, Nau
- 1992
(Show Context)
Citation Context ...cult. Despite the acknowledged difficulty of planning, it is only recently that researchers have begun to examine the computational complexity of planning problems and the reasons for that complexity =-=[5,3,16,17,22,20]-=-. This research has yielded some surprising results. For example, Gupta and Nau [16,17] have shown that contrary to prior expectations, deleted-condition interactions are easy to handle in blocks-worl... |

53 |
A Review of AI Planning Techniques
- Tate, Hendler, et al.
- 1990
(Show Context)
Citation Context ...nd IRI-9109755.1 Introduction Much planning research has been motivated, in one way or another, by the difficulty of producing complete and correct plans. For example, techniques such as abstraction =-=[27,6,24,31]-=- and task reduction [28,6,31] were developed in an effort to make planning more efficient, and concepts such as deleted-condition interactions were developed to describe situations which make planning... |

51 |
Complexity results for hierarchical task-network planning
- Erol, Hendler, et al.
- 1996
(Show Context)
Citation Context ...been the lack of a clear theoretical framework explaining what a HTN planning system is. To address this problem, some of us (together with Jim Hendler) are developing a formalization of HTN planning =-=[12,9]-=-. We intend to use this formalism to correctly define, explicate, and analyze various properties of HTN planning systems, such as soundness, completeness, complexity, and expressivity. Acknowledgement... |

44 |
Regression planning
- McDermott
- 1991
(Show Context)
Citation Context ... is whether a is necessarily/possibly true after execution of P . This question is especially important in partial-order planners such as NOAH [28], NONLIN [32], and SIPE [33]. For example, McDermott =-=[21]-=- says “unfortunately, partial orders have a big problem, that there is no way of deciding what is true for sure before a step without considering all possible step sequences consistent with the curren... |

38 | Complexity Results for Blocks-World Planning
- Gupta, Nau
- 1991
(Show Context)
Citation Context ...cult. Despite the acknowledged difficulty of planning, it is only recently that researchers have begun to examine the computational complexity of planning problems and the reasons for that complexity =-=[5,3,16,17,22,20]-=-. This research has yielded some surprising results. For example, Gupta and Nau [16,17] have shown that contrary to prior expectations, deleted-condition interactions are easy to handle in blocks-worl... |

30 | Planning in polynomial time: the SAS-PUBS class
- Bäckström, Klein
- 1991
(Show Context)
Citation Context ...range from polynomial time to pspace-complete. Chapman was the first to study issues relating to the undecidability of planning; we have discussed his work in detail in Section 3. Backstrom and Klein =-=[2]-=- found a class of planning problems called SAS-PUBS, for which planning can be done in polynomial time. Their planning formalism is somewhat different from ours: they make use of state variables that ... |

30 | When is planning decidable - Erol, Nau, et al. - 1992 |

27 | Merging separately generated plans with restricted inter[30
- Yang, Nau, et al.
(Show Context)
Citation Context ...t that given certain assumptions, one can reduce exponentially the time required to solve a conjoined-goal planning problem, provided that the individual goals are independent. Yang, Nau, and Hendler =-=[35]-=- have generalized this, showing that one can still exponentially reduce the time required for planning even if the goals are not independent, provided that only certain kinds of goal interactions are ... |

26 |
On the np-hardness of blocks world
- Chenoweth
- 1991
(Show Context)
Citation Context ...eveloped some efficient algorithms for merging plans to achieve multiple goals [34,35]. Complexity results have been developed for blocks-world planning by Gupta and Nau [16,17] and also by Chenoweth =-=[7]-=-. Gupta and Nau [16,17] have shown that the complexity of blocks-world planning arises not from deletedcondition interactions as was previously thought, but instead from enablingcondition interactions... |

14 |
Optimization of Multiple-Goal Plans with Limited Interactions
- Nau, Yang, et al.
- 1990
(Show Context)
Citation Context ...ided that only certain kinds of goal interactions are allowed. Under this same set of goal interactions, they have also developed some efficient algorithms for merging plans to achieve multiple goals =-=[34,35]-=-. Complexity results have been developed for blocks-world planning by Gupta and Nau [16,17] and also by Chenoweth [7]. Gupta and Nau [16,17] have shown that the complexity of blocks-world planning ari... |

13 |
Complexity Results for Extended Planning
- Bylander
- 1992
(Show Context)
Citation Context ...ed preconditions. Thus, if the operators are allowed to have delete lists, then whether or not they have negated preconditions has no effect on the complexity. 125 Related Work 5.1 Planning Bylander =-=[3,4]-=- has done several studies on the complexity of propositional planning. We have stated some of his results in Table 2. More recently, he has studied the complexity of propositional planning extended to... |

13 | Toward a general framework for hierarchical task-network planning
- Erol, Nau, et al.
- 1993
(Show Context)
Citation Context ...been the lack of a clear theoretical framework explaining what a HTN planning system is. To address this problem, some of us (together with Jim Hendler) are developing a formalization of HTN planning =-=[12,9]-=-. We intend to use this formalism to correctly define, explicate, and analyze various properties of HTN planning systems, such as soundness, completeness, complexity, and expressivity. Acknowledgement... |

7 |
Commitment strategies in planning
- Minton, Bresna, et al.
- 1991
(Show Context)
Citation Context ...cult. Despite the acknowledged difficulty of planning, it is only recently that researchers have begun to examine the computational complexity of planning problems and the reasons for that complexity =-=[5,3,16,17,22,20]-=-. This research has yielded some surprising results. For example, Gupta and Nau [16,17] have shown that contrary to prior expectations, deleted-condition interactions are easy to handle in blocks-worl... |

4 | On the complexity of possible truth
- Nau
- 1993
(Show Context)
Citation Context ...s a; and in return, he comes up with a polynomial-time algorithm for determining the necessary truth of a. However, his algorithm does not work correctly for establishing the possible truth of a (Nau =-=[23]-=- proves that problem is NP-hard). Chapman also proves that with conditional planning operators, establishing the necessary truth of a is co-NP-hard; and Dean and Boddy [8] prove a similar result with ... |

2 | Database Updates and AI Planning Domains
- Subrahmanian, Zaniolo
- 1993
(Show Context)
Citation Context ...14trivial task to extend this equivalence, because negation has different semantics for logic programming and planning. One recent result in this direction is the following: Subrahmanian and Zaniolo =-=[30]-=- have shown that STRIPS-style planning (with delete lists and negative preconditions) can be transformed, in polynomial time, to a class of logic programs with negation. Based on this transformation, ... |