Right, my comment retarding truth tables was only in reference to combinatorial logic. That said, pure circuit models of computations exist, and are interesting

Right, my comment retarding truth tables was only in reference to combinatorial logic. That said, pure circuit models of computations exist, and are interesting from a theoretical standpoint at least. They don't translate to hardware, though. As you noted doing arbitrary computation with (finite) circuits requires some type of feedback/sequential logic.