Structural Decomposition in FSM Design: Roots, Evolution, Current State—A Review

The review is devoted to methods of structural decomposition that are used for optimizing characteristics of circuits of finite state machines (FSMs). These methods are connected with the increasing the number of logic levels in resulting FSM circuits. They can be viewed as an alternative to methods of functional decompositions. The roots of these methods are analysed. It is shown that the first methods of structural decomposition have appeared in 1950s together with microprogram control units. The basic methods of structural decomposition are analysed. They are such methods as the replacement of FSM inputs, encoding collections of FSM outputs, and encoding of terms. It is shown that these methods can be used for any element basis. Additionally, the joint application of different methods is shown. The analysis of change in these methods related to the evolution of the logic elements is performed. The application of these methods for optimizing FPGA- based FSMs is shown. Such new methods as twofold state assignment and mixed encoding of outputs are analysed. Some methods are illustrated with examples of FSM synthesis. Additionally, some experimental results are represented. These results prove that the methods of structural decomposition really improve the characteristics of FSM circuits.