An unsatisfiable set of constraints is minimal if all its (strict) subsets are satisfiable. A number of forms of error diagnosis, including circuit error diagnosis and type error diagnosis, require finding all minimal unsatisfiable subsets of a given set of constraints (representing an error), in order to generate the best explanation of the error. In this paper we give algorithms for efficiently determining all minimal unsatisfiable subsets for any kind of constraints. We show how taking into account notions of independence of constraints and using incremental constraint solvers can significantly improve the calculation of these subsets.
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