Combinational equivalence checking methods and systems with internal don't cares

An equivalence checking method provides first and second logic functions. Don't care gates are inserted for don't care conditions in the first and second logic functions. The insertion of the don't care gates creates a first intermediate circuit and a second intermediate circuit. All 3DC gates of the first intermediate circuit are propagated and merged into a single 3DC gate when 3DC gates and SDC gates coexist in either of the first and second intermediate circuits. All 3DC gates of the second intermediate circuit are propagated and merged into a single 3DC gate when 3DC gates and SDC gates coexist in either of the first and second intermediate circuits. First and second circuit are produced in response to propagating and merging the 3DC gates. A combinational equivalence check is then performed of the first circuit to the second circuit under different equivalence relations.