Influence of state reduction on the number of state variables in race-free asynchronous sequential circuits

Generally, in synthesizing race-free asynchronous sequential circuits, state reduction and state assignment are performed in an independent way. In this paper it is shown that in performing state reduction, the number of variables for a race-free state assignment may increase. For an important class of asynchronous flow-tables, conditions are established by which the number of state variables does not increase or decrease when state reduction is performed.