Synthesis of four-phase asynchronous control circuits from pipeline dependency graphs

We propose a method of synthesizing pipeline controllers as four-phase asynchronous circuits from specifications described as two-phase dependency graphs. Pipeline two-phase dependency graphs are transformed into four-phase ones by applying a transformation rule to each simple loop in the graphs. Four-phase dependency graphs are easily mapped onto four-phase asynchronous control circuits. We also discuss some simplification of four-phase dependency graphs.