Optimal non-recursive method for finding a minimal subset satisfying an upward-closed property

摘要

According to an aspect, a method for providing a minimal explanation to a set of unsatisfiable constraints involves retrieving a minimal subset of constraints that remain together unsatisfiable. The method includes iterating over a list of n constraints, and building a minimal explanation to a set of unsatisfiable constraints by determining which constraint to add to the set of unsatisfiable constraints. Building includes accelerating by removing an increasing number of constraints until removed further constraints makes the set of constraints satisfiable. A dichotomic search is performed on the removed further constraints. The average observed distance is identified between successive constraints in the set of unsatisfiable constraints. A plurality of 2^k further constraints located in the list of constraints is removed at the average observed distance from the most recently added constraint. Testing whether a current selected subset is unsatisfiable is performed for the first log₂(n) added constraints.