Sequential Permissible Functions and their Application to Circuit Optimization

For sequential circuits the implementation freedom represented by combinational permissible functions (CPFs) and un-reachable states don't cares is not complete. We extend the concept of permissible functions to sequential circuits and introduce the sequential permissible functions (SPFs) to represent the complete freedom associated with a gate. We also study and compare the relationship between CPFs and SPFs. In general, the computation of the SPFs is more expensive than the computation of CPFs. We propose an algorithm that computes SPFs implicitly and is based on the well-known state traversal approach. The computed SPFs are used for sequential circuit optimization.