Implicit evaluation of encoding rotations for large FSMs

The problem of state assignment for finite state machines has been extensively studied by the synthesis community, targeting traditional criteria like area, performance, testability, or, more recently, power dissipation. State assignment algorithms targeting low power dissipation try to assign states so as to minimize the switching activity of the circuit, which is proportional, in CMOS circuits, to the power dissipation. However, for a given state assignment, there are exponentially many assignments that are exactly equivalent, obtained as rotations of the given assignment in the corresponding hyperspace. Proper selection of the representative encoding may significantly affect the area, and, indirectly, the dissipated power itself. In this paper we show the quantitative impact of these rotations on the final design in terms of area and power, and a criterion for evaluating the effect of the rotations when a symbolic model of the FSM is used.