## Pruning conformant plans by counting models on compiled d-DNNF representations (2005)

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Venue: | IN PROCEEDINGS OF THE 15TH INTERNATIONAL CONFERENCE ON AUTOMATED PLANNING AND SCHEDULING (ICAPS) |

Citations: | 19 - 7 self |

### BibTeX

@INPROCEEDINGS{Palacios05pruningconformant,

author = {Héctor Palacios and Adnan Darwiche and Blai Bonet and Héctor Geffner},

title = {Pruning conformant plans by counting models on compiled d-DNNF representations},

booktitle = {IN PROCEEDINGS OF THE 15TH INTERNATIONAL CONFERENCE ON AUTOMATED PLANNING AND SCHEDULING (ICAPS)},

year = {2005},

pages = {141--150},

publisher = {}

}

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### Abstract

Optimal planners in the classical setting are built around two notions: branching and pruning. SAT-based planners for example branch by trying the values of a selected variable, and prune by propagating constraints and checking consistency. In the conformant setting, a similar branching scheme can be used if restricted to action variables, but the pruning scheme must be modified. Indeed, pruning branches that encode inconsistent partial plans is not sufficient since a partial plan may be consistent and complete (covering all the action variables) and still fail to be a conformant plan. This happens indeed when the plan does not conform to some possible initial state or transition. A remedy to this problem is to use a criterion stronger than consistency for pruning. This is actually what we do in this paper where the consistency-based

### Citations

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Citation Context ...onential in the number of variables; the second in the number of states. The switch to symbolic representations as in (Cimatti, Roveri, & Bertoli 2004), where sets of states are represented by OBDDs (=-=Bryant 1992-=-), provides a handle on the first problem but not on the second that demands more informed admissible heuristic functions. Steps in this direction have been reported recently in (Cimatti, Roveri, & Be... |

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Citation Context ... a logical perspective, working on the theory encoding the problem, and branching on action literals until a valid plan is found. This approach, however, while so successful in the classical setting (=-=Kautz & Selman 1996-=-), 1 has not appeared to have worked well in the conformant setting, where pruning inconsistent partial plans is not sufficient. Indeed, a partial plan may be complete (covering all action variables) ... |

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Citation Context ...ompared to DNNF. For example, it is known that the DNF language is incomparable to the OBDD language from a succinctness viewpoint, even though DNF and OBDD are both strictly less succinct than DNNF (=-=Darwiche & Marquis 2002-=-). 4 This principle is also known as Boole’s expansion and Shannon’s expansion.s∧iαi is the product of the number of models of each conjunct αi, while the number of models of a DNNF ∨iαi that satisfie... |

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Citation Context ...cient. Deterministic DNNF Knowledge compilation is the area in AI concerned with the problem of mapping logical theories into suitable target languages that make certain desired operations tractable (=-=Selman & Kautz 1996-=-; Cadoli & Donini 1997). For example, propositional theories can be mapped into their set of Prime Implicates making the entailment test of clauses tractable (Reiter & de Kleer 1987). Similarly, the c... |

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Citation Context ... literal ∼ l to true when the model count MC(Tn ∧ l) is exactly 0. The inference, however, follows from the QBF formula associated with Tn encoding not only the planning domain but the planning task (=-=Rintanen 1999-=-). 8 are the frame axioms which may generate an exponential number of clauses. In order to avoid such explosion, each conjunction c k (a)i ∧ ai of a condition c k (a)i and the corresponding action ai,... |

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Citation Context ...DNNF Knowledge compilation is the area in AI concerned with the problem of mapping logical theories into suitable target languages that make certain desired operations tractable (Selman & Kautz 1996; =-=Cadoli & Donini 1997-=-). For example, propositional theories can be mapped into their set of Prime Implicates making the entailment test of clauses tractable (Reiter & de Kleer 1987). Similarly, the compilation into Ordere... |

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Citation Context ..., it will not necessarily do so on average. Indeed, the compilation of theories into OBDDs has been found useful in formal verification (Clarke, Grumberg, & Peled 1999) and more recently in planning (=-=Giunchiglia & Traverso 1999-=-). A more recent compilation language is Decomposable Negation Normal Form (DNNF) (Darwiche 2001). DNNFs support a rich set of polynomial–time operations, some of which are particularly suited to our ... |

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Citation Context ...ontents if not ordered. The optimal sequential plans minimize the number of gates, while the optimal parallel plans minimize the ‘time delay’ of the circuit. Only optimal plans for small n are known (=-=Knuth 1973-=-). The number of initial states is 2 n . The parameter n used ranges from 2 to 7. • Square-center: A robot without sensors moves in a room to north, south, east, and west, and its goal is to get to th... |

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Citation Context ...king consistency. In principle, the same two notions can and have been used in the conformant setting, where plans must map the initial situation into a goal situation in the presence of uncertainty (=-=Goldman & Boddy 1996-=-; Smith & Weld 1998). Still the results in the conformant setting have not been as strong, in part due to the higher complexity of the problem (Haslum & Jonsson 1999; Rintanen 2004a), in part, due to ... |

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Citation Context ...ion in the presence of uncertainty (Goldman & Boddy 1996; Smith & Weld 1998). Still the results in the conformant setting have not been as strong, in part due to the higher complexity of the problem (=-=Haslum & Jonsson 1999-=-; Rintanen 2004a), in part, due to the lack of sufficiently strong pruning criteria. In the context of directional branching schemes that search for plans by applying actions forward or backwards, the... |

17 |
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1 |
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Citation Context ...es, denoted as P roject(∆, V ), stands for the strongest formula over the V variables implied by ∆. Such formula is unique up to logical equivalence (the projection operation is dual to ‘forgetting’ (=-=Lin & Reiter 1994-=-)). • the model count of a formula ∆, denoted as MC(∆), stands for the number of truth assignments that satisfy the formula. With these two operations, and if we let F0 refer to the set of fluent vari... |