The main point in the design of content addressable memory would be under what conditions the state possessing the total information can attract all other states in the phase of the system. The problem can be formulated as a global asymptotic stability problem of Boolean dynamical systems. In this article we give a complete answer to this global asymptotic stability problem. The conditions employed involve the Hamming distance on the phase space ”0; 1•n as well as the spectral condition on the Jacobian Boolean matrix of Fx ”0; 1•n ! ”0; 1•n evaluated at each point of ”0; 1•n. This article furnishes a complete solution of the Boolean Markus–Yamabe problem.
