Theoretical considerations on the capabilities of crossbar switching by Hopfield networks

By the theory of the asymptotical stability and instability of solutions and nonsolutions previously presented by the author (1994), it is shown that optimal solutions of crossbar switch arbitration only without collisions of packets are always obtainable by solving n-rook problem by Hopfield networks, but that even they are not always obtainable if arbitration with maximum throughput is intended by solving inverse n-rook problem by Hopfield networks