## Probabilistic Propositional Planning: Representations and Complexity (1997)

Venue: | In Proceedings of the Fourteenth National Conference on Artificial Intelligence |

Citations: | 86 - 11 self |

### BibTeX

@INPROCEEDINGS{Littman97probabilisticpropositional,

author = {Michael L. Littman},

title = {Probabilistic Propositional Planning: Representations and Complexity},

booktitle = {In Proceedings of the Fourteenth National Conference on Artificial Intelligence},

year = {1997},

pages = {748--754},

publisher = {MIT Press}

}

### OpenURL

### Abstract

Many representations for probabilistic propositional planning problems have been studied. This paper reviews several such representations and shows that, in spite of superficial differences between the representations, they are "expressively equivalent," meaning that planning problems specified in one representation can be converted to equivalent planning problems in any of the other representations with at most a polynomial increase in the resulting representation and the number of steps needed to reach the goal with sufficient probability. The paper proves that the computational complexity of determining whether a successful plan exists for planning problems expressed in any of these representations is EXPTIME-complete and PSPACE-complete when plans are restricted to take a polynomial number of steps. Introduction In recent years, there has been an interest in solving planning problems that contain some degree of uncertainty. One form that this uncertainty has taken ...

### Citations

2429 | Computational complexity
- Papadimitriou
- 1994
(Show Context)
Citation Context ...Solving an mdp is P-complete (Papadimitriou & Tsitsiklis 1987) and it is often the case that succinctly represented versions of a problem are exponentially harder to solve than their simple versions (=-=Papadimitriou 1994-=-); this would imply EXPTIME-completeness if it were true in general. However, these intuitions are not enough---we need to prove that the problem is EXPTIME-complete. This is not a trivial task. A typ... |

1329 |
Markov Decision Processes: Discrete Stochastic Programming
- Puterman
- 1994
(Show Context)
Citation Context ...xistence problem is EXPTIME-complete. First, it seems harder than deterministic plan existence, which is PSPACEcomplete (Bylander 1994). Second, it is a compact form of the problem of solving an mdp (=-=Puterman 1994-=-). Solving an mdp is P-complete (Papadimitriou & Tsitsiklis 1987) and it is often the case that succinctly represented versions of a problem are exponentially harder to solve than their simple version... |

320 |
The complexity of markov decision processes
- Papadimitriou, Tsitsiklis
- 1987
(Show Context)
Citation Context ...t seems harder than deterministic plan existence, which is PSPACEcomplete (Bylander 1994). Second, it is a compact form of the problem of solving an mdp (Puterman 1994). Solving an mdp is P-complete (=-=Papadimitriou & Tsitsiklis 1987-=-) and it is often the case that succinctly represented versions of a problem are exponentially harder to solve than their simple versions (Papadimitriou 1994); this would imply EXPTIME-completeness if... |

307 | The computational complexity of propositional STRIPS planning
- BYLANDER
- 1994
(Show Context)
Citation Context ...sts that succeeds with sufficient probability. Although a great deal is known about the role of representation in and computational complexity of deterministic propositional planning (Backstrom 1995; =-=Bylander 1994-=-), probabilistic propositional planning has received much less attention. Several recent planners have been designed to manipulate probabilistic representations (Kushmerick, Hanks, & Weld 1995; Draper... |

277 | An algorithm for probabilistic planning - Kushmerick, Hanks, et al. - 1995 |

231 | Exploiting structure in policy construction - Boutilier, Dearden, et al. - 1995 |

210 | Probabilistic planning with information gathering and contingent execution - Draper, Hanks, et al. - 1994 |

161 | The Complexity of Stochastic Games
- Condon
- 1992
(Show Context)
Citation Context ...igure 1: ST representation for an action in G 4 number of actions in the planning problem. Such an mdp can be solved in exponential time (polynomial in the number of states) using linear programming (=-=Condon 1992-=-). If the optimal value of the initial state s 0 exceeds the threshold `, a valid plan exists. Next, we show how an instance of the G 4 game can be represented in ST. The state of the game is encoded ... |

92 | Planning under uncertainty: Structural assumptions and computational leverage - Boutilier, Dean, et al. - 1995 |

69 |
Abstraction and approximate decision-theoretic planning
- Dearden, Boutilier
- 1997
(Show Context)
Citation Context ...sitional planning has received much less attention. Several recent planners have been designed to manipulate probabilistic representations (Kushmerick, Hanks, & Weld 1995; Draper, Hanks, & Weld 1993; =-=Dearden & Boutilier 1997-=-; Boutilier, Dearden, & Goldszmidt 1995), which 1 Copyright c fl 1997, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. express a planning problem as a compact or ... |

68 | Abstraction and approximate decision theoretic planning
- Dearden, Boutilier
- 1997
(Show Context)
Citation Context ...sitional planning has received much less attention. Several recent planners have been designed to manipulate probabilistic representations (Kushmerick, Hanks, & Weld 1995; Draper, Hanks, & Weld 1993; =-=Dearden & Boutilier 1996-=-; Boutilier, Dearden, & Goldszmidt 1995; Boutilier & Dearden 1996), which express a planning problem as a compact or factored Markov decision process (mdp). This paper begins to explore the role of re... |

67 | Causal independence for probability assessment and inference using Bayesian networks
- Heckerman, Breese
- 1996
(Show Context)
Citation Context ..., but can have a substantial impact on best-case performance. This is because representational size is not all that matters. Just as the use of "noisy-or" nodes can speed up inference in bel=-=ief nets (Heckerman & Breese 1994-=-), representations and algorithms that exploit additional structure in propositional planning problems can be of great practical value. It is worth noting that the completeness results given in this p... |

38 | Approximating value trees in structured dynamic programming
- Boutilier, Dearden
- 1996
(Show Context)
Citation Context ...t planners have been designed to manipulate probabilistic representations (Kushmerick, Hanks, & Weld 1995; Draper, Hanks, & Weld 1993; Dearden & Boutilier 1996; Boutilier, Dearden, & Goldszmidt 1995; =-=Boutilier & Dearden 1996-=-), which express a planning problem as a compact or factored Markov decision process (mdp). This paper begins to explore the role of representation in probabilistic planning. The first section introdu... |

31 | Expressive equivalence of planning formalisms
- Bäckström
- 1995
(Show Context)
Citation Context ...ether a plan exists that succeeds with sufficient probability. Although a great deal is known about the role of representation in and computational complexity of deterministic propositional planning (=-=Backstrom 1995-=-; Bylander 1994), probabilistic propositional planning has received much less attention. Several recent planners have been designed to manipulate probabilistic representations (Kushmerick, Hanks, & We... |

19 | The complexity of plan existence and evaluation in probabilistic domains - Goldsmith, Littman, et al. - 1997 |

5 | The complexity of deterministically observable finite-horizon Markov decision processes - Goldsmith, Lusena, et al. - 1996 |

4 | The complexity of unobservable finite-horizon Markov decision processes - Mundhenk, Goldsmith, et al. - 1996 |

2 |
Games against nature (extended abstract
- Papadimitriou
- 1983
(Show Context)
Citation Context ...-x i -true y i-1 -set x i -set T F T x -set y i T F y -set T 1/2 T F pick-y i x i -set y i -set T F T Figure 2: ST representation for two QBF actions been studied in the "games against nature&quo=-=t; model (Papadimitriou 1983-=-). Theorem 2 The polynomial-horizon plan-existence problem for ST is PSPACE-complete. Proof: To show PSPACE-completeness, we show that the problem can be solved in polynomial space and that the PSPACE... |