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Unate and binate covering problems are a subclass of general integer linear programming problems with which several problems in logic synthesis, such as two-level logic minimization and technology mapping, are formulated. Previous branch-and-bound methods for solving these problems exactly use lower bounding techniques based on finding maximal independent sets. In this paper, we examine lower bounding techniques based on linear programming relaxation (LPR) for the covering problem. We show that a combination of traditional reductions (essentiality and dominance) and incremental computation of LPR-based lower bounds can exactly solve difficult covering problems orders of magnitude faster than traditional methods.