Redundant Sudoku Rules
This work addresses a theoretical problem in constraint satisfaction and logic programming, but it is incremental as it builds on known Sudoku rules without broader ML/AI implications.
The paper tackled the problem of identifying redundant constraints in Sudoku by proving that many subsets of six of the twenty-seven 'big' all_different constraints are redundant and that six is the maximum number that can be removed while maintaining equivalence, with a conjecture for binary inequality constraints.
The rules of Sudoku are often specified using twenty seven \texttt{all\_different} constraints, referred to as the {\em big} \mrules. Using graphical proofs and exploratory logic programming, the following main and new result is obtained: many subsets of six of these big \mrules are redundant (i.e., they are entailed by the remaining twenty one \mrules), and six is maximal (i.e., removing more than six \mrules is not possible while maintaining equivalence). The corresponding result for binary inequality constraints, referred to as the {\em small} \mrules, is stated as a conjecture.