Theoretical analysis of hysteresis neural network solving N-Queens problems

We propose a hysteresis neural network system solving NP-hard optimization problems, the N-Queens Problem. The continuous system with binary outputs searches a solution of the problem without energy function. The output vector corresponds to a complete solution when the output vector becomes stable. That is, this system does never become stable without satisfying the constraints of the problem. Through it is very hard to remove limit cycles completely from this system, we can propose a new method to reduce the possibility of limit cycle by controlling time constants.