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A set of constraints that cannot be simultaneously satisfied is over-constrained. Minimal relaxations and minimal explanations for over-constrained problems find many practical uses. For Boolean formulas, minimal relaxations of over-constrained problems are referred to as Minimal Correction Subsets (MCSes). MCSes find many applications, including the(More)
Minimal explanations of infeasibility find a wide range of uses. In the Boolean domain, these are referred to as Minimal Unsatisfiable Subsets (MUSes). In some settings , one needs to enumerate MUSes of a Boolean formula. Most often the goal is to enumerate all MUSes. In cases where this is computationally infeasible, an alternative is to enumerate some(More)
The problem of enumerating minimal unsatisfiable subsets (MUSes) of an infeasible constraint system is challenging due first to the complexity of computing even a single MUS and second to the potentially intractable number of MUSes an instance may contain. In the face of the latter issue, when complete enumeration is not feasible, a partial enumeration of(More)
Minimal explanations of infeasibility are of great interest in many domains. In propositional logic, these are referred to as Minimal Unsatisfiable Subsets (MUSes). An unsatisfiable formula can have multiple MUSes, some of which provide more insights than others. Different criteria can be considered in order to identify a good minimal explanation. Among(More)
Formula compilation by generation of prime implicates or implicants finds a wide range of applications in AI. Recent work on formula compilation by prime implicate/implicant generation often assumes a Conjunctive/Disjunctive Normal Form (CNF/DNF) representation. However, in many settings propositional formulae are naturally expressed in non-clausal form.(More)
In this paper we perform a preliminary investigation into the application of sampling-based search algorithms to satisfiability testing of propositional formulas in Conjunctive Normal Form (CNF). In particular, we adapt the Upper Confidence bounds applied to Trees (UCT) algorithm [5] which has been successfully used in many game playing programs including(More)
Even when it has been shown that no solution exists for a particular constraint satisfaction problem, one may still aim to restore consistency by relaxing the minimal number of constraints. In the context of a Boolean formula like SAT, such a relaxation is referred to as a Minimal Correction Subset (MCS). In the context of SAT, identifying MCSs for an(More)
In this paper, we investigate the feasibility of applying algorithms based on the Uniform Confidence bounds applied to Trees [12] to the satisfiability of CNF formulas. We develop a new family of algorithms based on the idea of balancing exploitation (depth-first search) and exploration (breadth-first search), that can be combined with two different(More)