Set selection dynamical system neural networks with partial memories, with applications to Sudoku and KenKen puzzles

After reviewing set selection and memory model dynamical system neural networks, we introduce a neural network model that combines set selection with partial memories (stored memories on subsets of states in the network). We establish that feasible equilibria with all states equal to ± 1 correspond to answers to a particular set theoretic problem. We show that KenKen puzzles can be formulated as a particular case of this set theoretic problem and use the neural network model to solve them; in addition, we use a similar approach to solve Sudoku. We illustrate the approach in examples. As a heuristic experiment, we use online or print resources to identify the difficulty of the puzzles and compare these difficulties to the number of iterations used by the appropriate neural network solver, finding a strong relationship.