In this paper, ManySAT a new portfolio-based parallel SAT solver is thoroughly described. The design of ManySAT benefits from the main weaknesses of modern SAT solvers: their sensitivity to parameter tuning and their lack of robustness. ManySAT uses a portfolio of complementary sequential algorithms obtained through careful variations of the standard DPLL algorithm. Additionally, each sequential algorithm shares clauses to improve the overall performance of the whole system. This contrasts with most of the parallel SAT solvers generally designed using the divide-and-conquer paradigm. Experiments on many industrial SAT instances, and the first rank obtained by ManySAT in the parallel track of the 2008 SAT-Race clearly show the potential of our design philosophy.

Abstract. In this paper, a new pre-processing step is proposed in the resolution of SAT instances, that recovers and exploits structural knowledge that is hidden in the CNF. It delivers an hybrid formula made of clauses together with a set of equations of the form y = f (x1, . . . , xn) where f is a standard connective operator among (∨, ∧, ⇔) and where y and xi are boolean variables of the initial SAT instance. This set of equations is then exploited to eliminate clauses and variables, while preserving satisfiability. These extraction and simplification techniques allowed us to implement a new SAT solver that proves to be the most efficient current one w.r.t. several important classes of instances.

Conflict driven clause learning, one of the most important component of modern SAT solvers, is also recognized as very important in parallel SAT solving. Indeed, it allows clause sharing between multiple processing units working on related (sub-)problems. However, without limitation, sharing clauses might lead to an exponential blow up in communication or to the sharing of irrelevant clauses. This paper, proposes two innovative policies to dynamically adjust the size of shared clauses between any pair of processing units. The first approach controls the overall number of exchanged clauses whereas the second additionally exploits the relevance quality of shared clauses. Experimental results show important improvements of the state-of the-art parallel SAT solver.

In this paper 1. , nogood recording is investigated for CSP within the randomization and restart framework. Our goal is to avoid the same situations to occur from one run to the next ones. More precisely, nogoods are recorded when the current cutoff value is reached, i.e. before restarting the search algorithm. Such a set of nogoods is extracted from the last branch of the current search tree and exploited using the structure of watched literals originally proposed for SAT. We prove that the worst-case time complexity of extracting such nogoods at the end of each run is only O(n 2 d) where n is the number of variables of the constraint network and d the size of the greatest domain, whereas for any node of the search tree, the worst-case time complexity of exploiting these nogoods to enforce Generalized Arc Consistency (GAC) is O(n|B|) where |B| denotes the number of recorded nogoods. As the number of nogoods recorded before each new run is bounded by the length of the last branch, the total number of recorded nogoods is polynomial in the number of restarts. Interestingly, we show that when the minimization of the nogoods is envisioned with respect to an inference operator φ, it is possible to directly identify some nogoods that cannot be minimized. For φ = AC (i.e. for MAC), the worst-case time complexity of extracting minimal nogoods is slightly increased to O(en 2 d 3) where e is the number of constraints of the network. Experimentation over a wide range of CSP instances using a generic stateof-the-art CSP solver demonstrates the effectiveness of this approach. Recording nogoods (and in particular, minimal nogoods) from restarts significantly improves the robustness of the solver.

No abstract

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.

No abstract

Abstract. The usual way for solving constraint satisfaction problems is to use a backtracking algorithm. One of the key factors in its e ciency is the rule it will use to decide on which v ariable to branch next (namely, the variable ordering heuristics). In this paper, we attempt to give a general formulation of dynamic variable ordering heuristics that take i n to account the properties of the neighborhood of the variable. An empirical evaluation on random CSPs and a sample of real instances shows that the obtained heuristics can improve signi cantly the current b e s t o n e s .