Computation of Flexibility in Sequential Networks
There is a long history of resynthesizing an FSM, given its surrounding environment. Much of the work was modeled after results for combinational networks. Thus input sequential don’t cares and output sequential don’t cares were defined in analogy to satisfiability and observability don’t cares. For example, input sequential don’t cares were defined as input sequences that can never happen at a state because of the FSM input environment. An elegant theory was provided by Kim and Newborn for treating the case of a cascade of two FSMs. This is discussed in Sect. 10.1 as well as an extension by Wang and Brayton in Sect. 10.2. These results provide reasonable computational procedures and can be used for resynthesis of an FSM. However, attempts at extending to output sequential don’t cares became overly complicated and were unsuccessful. It was surprising then that Watanabe came up with a computation for the full flexibility for an FSM embedded in an environment, which captures all input and output sequential don’t cares. This was called the “E-machine” and was constructed by a somewhat complicated construction. It became clear later that this construction essentially modeled the subset construction. Now we know that this full flexibility embodied by the E-machine is simply the largest FSM solution obtained by language solving, and a simpler construction is the one given in this book and discussed in this chapter in more detail.