Solving sudoku puzzles by using hopfield neural networks

Authors:
V. Mladenov;P. Karampelas;C. Pavlatos;E. Zirintsis
Affiliations:
Department of Theoretical Electrical Engineering, Technical University of Sofia, Bulgaria;IT Faculty, Hellenic American University, Athens, Greece;IT Faculty, Hellenic American University, Athens, Greece;IT Faculty, Hellenic American University, Athens, Greece
Venue:
ICACM'11 Proceedings of the 2011 international conference on Applied & computational mathematics
Year:
2011

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Neural Networks for Optimization and Signal Processing

Neural Networks for Optimization and Signal Processing
Searching for memories, sudoku, implicit check bits, and the iterative use of not-always-correct rapid neural computation

Neural Computation

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Abstract

In this paper two different approaches to solve Sudoku puzzles with neural networks are presented. The first approach is proposed by J.J. Hopfield. He tries to solve the Sudoku puzzle with help of a Hopfield network and treated the problem as an integer optimization problem that is also used for the solution of the well known Traveling Salesmen Problem (TSP). Second solution uses the Hopfield network with an extension, called co-processor. Since neural networks can exactly solve linear programming problems, such a network can be used as co-processor to improve the performance of the Hopfield network. Combination of both networks, where the Hopfield network was used first, was able to solve a lot of puzzles.