Computing observability don't cares efficiently through polarization

A new method is presented to compute the exact observability don't cares (ODCs) for multiple-level combinational circuits. A new mathematical concept, called polarization, is introduced. Polarization captures the essence of ODC calculation on the otherwise difficult points of reconvergence. It makes it possible to derive the ODC of a node from the ODCs of its fanouts with a very simple formula. Experimental results for the 39 largest MCNC benchmark examples show that the method is able to compute the ODC set (expressed as a Boolean network) for all but one circuit in at most a few seconds.