Another group of methods is related to decomposing the machine into a group of machines. Various approaches have been investigated. The classical methods, based on partition theory, seek in general certain partitions that permit description of a machine as a parallel, cascade or parallel/cascade composition of other machines. Such procedure can be done recursively. Unfortunately, such types of decomposition are very laborious to find and their nontrivial cases occur rarely for industrial machines. Some useful variants of classical theories discuss decomposition with use of important blocks like shift registers and counters.
New methods of decomposition try to use general graph partitioning methods [Kern 70] to partition a state graph. Such methods are used in practical systems as a neccessity, but their behavior seems to be unsatisfactory. Yet another group of methods assumes certain structure of the realization of the machine, for instance a microprogrammed unit, in which some outputs from the FSM are on the address input of some multiplexer and control selection of input signals to this FSM (the multiplexer's output is one of inputs of a FSM). Separate PLAs are realized for encoding of input and encoding of output signals. The main PLA realizing excitation and output functions is partitioned into many PLAs. These approaches combined can yield many various decomposed structures with essentially different realization costs.
Another possible approach is to create methods, that are particularly suitable for some selected method of machine's realization. For instance, methods of FSM design especially suitable for PLA minimization are discussed in [79, 117, 132, 166, 133].