Computers in Industry - Special issue: co-operation in manufacturing systems, CIM at work
Decomposable negation normal form
Journal of the ACM (JACM)
Consistency restoriation and explanations in dynamic CSPs----application to configuration
Artificial Intelligence
Effective Interaction Principles for Online Product Search Environments
WI '04 Proceedings of the 2004 IEEE/WIC/ACM International Conference on Web Intelligence
QUICKXPLAIN: preferred explanations and relaxations for over-constrained problems
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Representative explanations for over-constrained problems
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Journal of Artificial Intelligence Research
Boosting a complete technique to find MSS and MUS thanks to a local search oracle
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Identifying conflicts in overconstrained temporal problems
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Computing explanations and implications in preference-based configurators
ERCIM'02/CologNet'02 Proceedings of the 2002 Joint ERCIM/CologNet international conference on Constraint solving and constraint logic programming
Inference-based constraint satisfaction supports explanation
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
On finding all minimally unsatisfiable subformulas
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Discovery of minimal unsatisfiable subsets of constraints using hitting set dualization
PADL'05 Proceedings of the 7th international conference on Practical Aspects of Declarative Languages
cmMUS: a tool for circumscription-based MUS membership testing
LPNMR'11 Proceedings of the 11th international conference on Logic programming and nonmonotonic reasoning
On deciding MUS membership with QBF
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
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In many real-world settings, e.g. product configuration, constraint satisfaction problems are compiled into automata or binary decision diagrams, which can be seen as instances of Darwiche's negation normal form. In this paper we consider settings in which a foreground set of constraints can be added to a set of consistent background constraints, that are compactly represented in a compiled form. When the set of foreground constraints introduces inconsistencies with the background constraints we wish to find relaxations of the problem by identifying the subset of the foreground constraints that do not introduce inconsistency; such a subset is called a relaxation. This paper is organised in two parts. First, two novel algorithms for finding relaxations based on automata are presented. They find the relaxation that is consistent with the largest (or smallest) number of solutions from amongst the longest ones (first algorithm), or from amongst the set-wise maximal ones (second algorithm). Then, we generalise our results by identifying the properties that the target compilation language must have for our approach to apply. Finally, we show empirically that on average our algorithms can be more than 500 times faster than a current state-of-the-art algorithm.