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Improving redundancy addition and removal using unreachable states for sequential circuits

Redundancy Addition and Removal (RAR), one of the major combinational logic perturbation techniques, has been shown to be very useful for many EDA optimization tasks. However, all the currently known RAR techniques did not analyze and make use of unreachable states, which are abundant in sequential circuits. These unreachable states can be considered as input don't cares and can add an extra flexibility in locating alternative wires. In this paper, we study the fundamental theory and propose a reasoning scheme for locating alternative wires without performing wasteful redundancy tests. To explore the deeper effect of unreachable states, the concept is extended to illegal assignments and the fault independent redundancy identification is applied on illegal assignments to find flexibilities introduced by unreachable states. On the experiments carried for both MCNC and industry benchmarks, it is shown that using such an idea, a remarkable increase of more than 100% (averagely) in the number of alternative wires can be found, which should be quite useful as most of today's practical circuits are sequential.