Des ensembles Horn strong backdoor aux ensembles ordonnés strong backdoor

L'identification et l'exploitation de structures cachées dans un problème est reconnue comme étant un moyen fondamental pour contrecarrer l'explosion combinatoire de sa résolution. Récemment, une structure particulière appelée (strong) backdoor a été identifiée pour le problème de satisfaisabilité de formule CNF (SAT). Certaines connexions entre les ensembles strong backdoor et la difficulté intrinsèque des problèmes SAT ont été mises en évidence, permettant une meilleure approximation de la borne de complexité en temps dans le pire des cas. On peut calculer des ensembles strong backdoor pour chaque classe polynomiale. Dans [Parisetals06], une méthode d'approximation d'ensembles strong backdoor pour la classe des formules de Horn a été proposée. Cette approximation est réalisée en deux étapes. Dans un premier temps, on calcule le meilleur Horn renommage du point de vue du nombre de clauses de Horn de la CNF de départ. Ensuite on extrait un ensemble Horn strong backdoor de la partie non Horn de la formule renommée. Dans cet article, nous proposons de calculer des ensembles Horn strong backdoor en utilisant le même procédé mais en minimisant le nombre de littéraux positifs dans la partie non Horn de la formule renommée au lieu du nombre de clauses. Puis nous étendons cette méthode à la classe des formules ordonnée [benoist99] qui est une extension de la classe des formules de Horn. Cette méthode nous garantit l'obtention d'ensembles Ordonné strong backdoor de taille plus petite ou égale à ceux des ensembles Horn strong backdoor (jamais plus grande). Les résultats expérimentaux montrent que ces nouvelles méthodes permettent de réduire la taille des ensembles strong backdoor sur certaines instances et que leur exploitation permet également d'améliorer les performances des solveurs SAT

Tools and Algorithms for the Construction and Analysis of Systems

This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers

Graphical Models and Symmetries : Loopy Belief Propagation Approaches

Whenever a person or an automated system has to reason in uncertain domains, probability theory is necessary. Probabilistic graphical models allow us to build statistical models that capture complex dependencies between random variables. Inference in these models, however, can easily become intractable. Typical ways to address this scaling issue are inference by approximate message-passing, stochastic gradients, and MapReduce, among others. Exploiting the symmetries of graphical models, however, has not yet been considered for scaling statistical machine learning applications. One instance of graphical models that are inherently symmetric are statistical relational models. These have recently gained attraction within the machine learning and AI communities and combine probability theory with first-order logic, thereby allowing for an efficient representation of structured relational domains. The provided formalisms to compactly represent complex real-world domains enable us to effectively describe large problem instances. Inference within and training of graphical models, however, have not been able to keep pace with the increased representational power. This thesis tackles two major aspects of graphical models and shows that both inference and training can indeed benefit from exploiting symmetries. It first deals with efficient inference exploiting symmetries in graphical models for various query types. We introduce lifted loopy belief propagation (lifted LBP), the first lifted parallel inference approach for relational as well as propositional graphical models. Lifted LBP can effectively speed up marginal inference, but cannot straightforwardly be applied to other types of queries. Thus we also demonstrate efficient lifted algorithms for MAP inference and higher order marginals, as well as the efficient handling of multiple inference tasks. Then we turn to the training of graphical models and introduce the first lifted online training for relational models. Our training procedure and the MapReduce lifting for loopy belief propagation combine lifting with the traditional statistical approaches to scaling, thereby bridging the gap between statistical relational learning and traditional statistical machine learning

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum