Sudoku associative memory

Abstract

This work presents bipolar neural systems for check-rule embedded pattern restoration, fault-tolerant information encoding and Sudoku memory construction and association. The primitive bipolar neural unit is generalized to have internal fields and activations, which are respectively characterized by exponential growth and logistic differential dynamics, in response to inhibitory and excitatory stimuli. Coupling extended bipolar units induces multi-state artificial Potts neurons which are interconnected with inhibitory synapses for Latin square encoding, K-alphabet Latin square encoding and Sudoku encoding. The proposed neural dynamics can generally restore Sudoku patterns from partial sparse clues. Neural relaxation is based on mean field annealing that well guarantees reliable convergence to ground states. Sudoku associative memory combines inhibitory interconnections of Sudoku encoding with Hebb’s excitatory synapses of encoding conjunctive relations among active units over memorized patterns. Sudoku associative memory is empirically shown reliable and effective for restoring memorized patterns subject to typical sparse clues, fewer partial clues, dense clues and perturbed or damaged clues. On the basis, compound Sudoku patterns are further extended to emulate complex topological information encoding.