## Procedural Reasoning in Constraint Satisfaction (1996)

Citations: | 15 - 5 self |

### BibTeX

@TECHREPORT{Jónsson96proceduralreasoning,

author = {Ari K. Jónsson and Matthew L. Ginsberg},

title = {Procedural Reasoning in Constraint Satisfaction},

institution = {},

year = {1996}

}

### OpenURL

### Abstract

For many constraint satisfaction problems, there are well known, fast algorithms and functions that solve parts of the problem. Using these methods directly to solve the subproblems significantly speeds up the solving process. Unfortunately, doing this has usually required the solver to be changed, or the correctness criteria to be re-examined. We describe a general mechanism to use procedures with almost any search engine, such that it is easy to add any procedures without changing the engine. Furthermore, the framework is formally defined, which allows us to prove conditions that are sufficient to guarantee systematicity and completeness for search engines using procedures. 1 Introduction For many constraint satisfaction problems there are simple functional relations (e.g. arithmetic equations) and simple subproblems (e.g. linear equations with unknowns) that can be solved quickly, using simple algorithms. Needless to say, taking advantage of such algorithms can significantly decrea...

### Citations

10921 | Computers and Intractability: A Guide to the Theory of NP-Completeness - Garey, Johnson |

1075 |
A computing procedure for quantification theory
- Davis, Putnam
- 1960
(Show Context)
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- Dechter, Meiri, et al.
- 1991
(Show Context)
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- 1992
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- 1995
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Enhancement schemes for constraint processing: backjumping, learning, and cutset decomposition
- Dechter
- 1990
(Show Context)
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- 1993
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- Gaschnig
- 1979
(Show Context)
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- Sadeh
- 1991
(Show Context)
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- Kambhampati, Knoblock, et al.
- 1995
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- Ginsberg, Harvey
- 1992
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- Korf
- 1996
(Show Context)
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- Harvey
- 1995
(Show Context)
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- Prosser
- 1993
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- 1988
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Citation Context ...r using correct procedures. The third condition turns out to be satisfied by almost any systematic engine, in particular depth-first search, limited discrepancy search, relevance-bounded backtracking =-=[20]-=-, size-bounded backtracking and dynamic backtracking all satisfy this condition. 3.4 Overview of Correctness Results 3.4.1 Introduction In this chapter we have provided a set of conditions that have b... |

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Citation Context ...roblems, and thus required a search engine to solve these problems efficiently. The system, called COPS [14], implements a newly developed approach to generative planning, called approximate planning =-=[13]-=-. This approach is based on refining two planset descriptions, one describing those plans that can be guaranteed to succeed and another describing those plans that may succeed. If the first set can be... |

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Citation Context ...ious approaches have been suggested for exploiting this separation. Some rely on constraint propagation methods for checking the constraint satisfaction problems generated during the planning process =-=[19, 41]-=-, while others rely on higher level through the space of possible action selections, for instance by limiting the number of action instances [22, 23]. The approach that we study here is based on a new... |

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- 1974
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Citation Context ...pletion, we were made aware of an system that generated constraint satisfaction problems as subproblems, and thus required a search engine to solve these problems efficiently. The system, called COPS =-=[14]-=-, implements a newly developed approach to generative planning, called approximate planning [13]. This approach is based on refining two planset descriptions, one describing those plans that can be gu... |

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Citation Context ...ting inference rule is not complete. This has led to the development of procedural reasoning techniques that are not based on attachments; the most notable being the concept of specialized procedures =-=[35]-=-. Although the problem with incompleteness in theorem proving does not appear in constraint satisfaction, the specialized procedures have another quality that eliminates one of the shortcomings of pro... |

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Citation Context ...clearly makes refinement search unsuitable for reasoning about the effects of procedures on search engines. The approach essentially boils the problem down to state-space search. Global search theory =-=[36, 37]-=- is a framework that is similar to refinement search; it defines sets of solution candidates and operators that either split the sets or prune them. The main advantages are that the pruning operators ... |

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Citation Context ...eviously discussed approaches, except that it does allow us to describe the search control to a certain extent. The fundamental idea behind it is the decomposition of constraint satisfaction problems =-=[8]-=-. Starting with the given domain for each variable, progress is made by eliminating values from domains; typically this is done by splitting some domain into two or more parts. When each domain has be... |

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Citation Context ...arative information that is then used by a standard search engine. This approach is typically used for solvers that have a well-defined input language, such as the popular satisfiability engines wsat =-=[33]-=- and tableau. To see what these kinds of translations may look like, let us look at one that was developed for using the sample scheduling procedure with satisfiability engines. The translation is bas... |

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Citation Context ...clearly makes refinement search unsuitable for reasoning about the effects of procedures on search engines. The approach essentially boils the problem down to state-space search. Global search theory =-=[36, 37]-=- is a framework that is similar to refinement search; it defines sets of solution candidates and operators that either split the sets or prune them. The main advantages are that the pruning operators ... |