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

A computer-implemented method for providing a minimal explanation to a set of unsatisfiable constraints, the computer-implemented method involving retrieving by a processor of a computer a minimal subset of constraints that remain together unsatisfiable, the computer-implemented method comprising:

• iterating over a list of n constraints from a first one of the list of constraints to an nth one of the list of constraints;
• and
• building a minimal explanation to a set of unsatisfiable constraints by determining by the processor which constraint to add to the set of unsatisfiable constraints, the building comprising:
• accelerating by removing an increasing number of constraints until a removed plurality of further constraints makes a set of constraints satisfiable;
• performing a dichotomic search on the removed plurality of further constraints;
• identifying an average observed distance between successive constraints in the set of unsatisfiable constraints;
• removing a plurality of 2k further constraints located in the list of constraints at the average observed distance from a most recently added constraint;
• and
• for the first log2(n) added constraints, testing whether a current selected subset is unsatisfiable.