Using Connectivity and Spectral Methods to Characterize the Structure of Sequential Logic Circuits

Representing finite state systems by means of finite state machines is a common approach in VLSI circuit design. BDD-based algorithms have made possible the manipulation of FSMs with very large state spaces; however, when the representation of the set of reachable states grows too much, the original FSM is no longer manageable as a whole, and it needs to be decomposed into smaller sub-machines. Structural analysis of the circuit from which the FSM has been extracted has shown to be very effective to determine good state variable partitions which induce FSM decomposition for logic synthesis and formal verification applications. In this paper we propose FSM analysis techniques based on connectivity and spectral characteristics of the state machine which take into account the mutual dependency of the state variables, but which are no longer dependent on the structure of the underlying circuit; therefore, they may be used in a context different from sequential logic optimization and FSM verification. Experimental results are presented and discussed for the mcnc'91 FSM benchmarks and for the iscas'89 sequential circuits.