Abstract. In this paper, we introduce a new problem, called Top-k SAT, that consists in enumerating the Top-k models of a propositional formula. A Top-k model is defined as a model with less than k models preferred to it with respect to a preference relation. We show that Top-k SAT generalizes two well-known problems: the partial Max-SAT problem and the problem of computing minimal models. Moreover, we propose a general algorithm for Top-k SAT. Then, we give the first application of our declarative framework in data mining, namely, the problem of enumerating the Top-k frequent closed itemsets of length at least min (FCIM k min ). Finally, to show the nice declarative aspects of our framework, we encode several other variants of FCIM k min into the Top-k SAT problem.

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In this paper, we propose a SAT-based encoding for the problem of discovering frequent, closed and maximal patterns in a sequence of items and a sequence of itemsets. Our encoding can be seen as an improvement of the approach proposed in [8] for the sequences of items. In this case, we show experimentally on real world data that our encoding is significantly better. Then we introduce a new extension of the problem to enumerate patterns in a sequence of itemsets. Thanks to the flexibility and to the declarative aspects of our SAT-based approach, an encoding for the sequences of itemsets is obtained by a very slight modification of that for the sequences of items.

In this paper, we revisit an important issue of CDCL-based SAT solvers, namely the learned clauses database management policies. Our motivation takes its source from a simple observation on the remarkable performances of both random and size-bounded reduction strategies. We first derive a simple reduction strategy, called Size-Bounded Randomized strategy (in short SBR), that combines maintaining short clauses (of size bounded by k), while deleting randomly clauses of size greater than k. The resulting strategy outperform the state-of-the-art on SAT instances taken from the SAT competitions 2013 and 2018, and remains competitive on a broad range of SAT instances of the SAT Competition 2014. Reinforced by the interest of keeping short clauses, we propose several new dynamic variants, and we discuss their performance. We also propose different ways for adjusting dynamically the size-bounded parameter of the strategy.