Invariant States and Redundant Logic in Synchronous Sequential Circuits

The concept of invariant states of synchronous sequential circuits is defined. An invariant state is incompletely specified (i.e., it is a cube), and its specified state variables remain constant under any input vector. Invariant states provide a method to identify redundant logic, which may not be identified based on redundant stuck-at faults. A procedure for finding invariant states with maximal numbers of specified state variables is described. The process of finding redundant logic based on an invariant state is explained. Experimental results show that several large benchmark circuits have invariant states with large numbers of specified state variables, explaining why these circuits are untestable. Properties of invariant states in synchronizable circuits are also discussed