FSM Re-Engineering for Low Power State Encoding

Finite State Machine (FSM) synthesis traditionally starts with state minimization and state encoding, which provide codes of minimal length to the FSM with minimal number of states. Recently, there have been studies on encoding with nonminimal length and synthesis on non-minimized FSM. In this paper, we propose the framework of FSM re-engineering, which starts with synthesizing the original FSM, followed by re-constructing a functionally equivalent but topologically different FSM, and ends with another round of FSM synthesis on the newly constructed FSM. This gives us a larger solution space that consists of synthesis solutions to any of the functionally equivalent FSMs rather than the original FSM only. Guided by the result of the first round FSM synthesis, the solution space exploration process is rapid and costefficient. This framework enables us to find better synthesis solutions, sometimes even better than the optimal ones in the original FSM. We demonstrate this framework on low power state encoding, where we first use POW3 to assign code to each FSM benchmark, then we re-construct the FSM by introducing new states selectively, the re-constructed FSM is encoded again by POW3. Experiments on MCNC benchmarks show that we are able to reduce the FSM’s switching activity by 6.0% on average. This results in an average 9.4% energy reduction at the cost of 1.3% area increase in SIS simulation, which is better than other non-minimal length low power encoding techniques on comparable cases. More interestingly, when we obtain the optimal coding via an integer linear programming formulation on small size benchmarks, we find that POW3-encoded original FSMs are 27.0% worse than the optimal, but this number drops to 10.1% when we apply POW3 to the re-engineered FSMs.