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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)
Algorithms for extraction of Minimally Unsatisfiable Subformulas (MUSes) of CNF formulas find a wide range of practical applications, including product configuration, knowledge-based validation, hardware and software design and verification. This paper describes the MUS extractor MUSer2. MUSer2 implements a wide range of MUS extraction algorithms,(More)
Programs for the Boolean satisfiability problem (SAT), i.e., SAT solvers, are nowadays used as core decision procedures for a wide range of combinatorial problems. Advances in SAT solving during the last 10–15 years have been spurred by yearly solver competitions. In this article, we report on the main SAT solver competition held in 2012, SAT Challenge(More)
Detection and elimination of redundant clauses from propositional formulas in Conjunctive Normal Form (CNF) is a fundamental problem with numerous application domains, including AI, and has been the subject of extensive research. Moreover, a number of recent applications motivated various extensions of this problem. For example, unsatisfiable formulas(More)
The importance and impact of the Boolean satisfiability (SAT) problem in many practical settings is well-known. Besides SAT, a number of computational problems related with Boolean formulas find a wide range of practical applications. Concrete examples for CNF formulas include computing prime implicates (PIs), minimal models (MMs), minimal unsatisfiable(More)