We introduce a new combinatorial technique to obtain relativized separations of certain complexity classes related to the idea of counting, like PP, G (exact counting), and ¿P (parity). To demonstrate its usefulness we present three relativizations separating NP from G, NP from ¿P and ¿P from PP. Other separations follow from these results, and as a consequence we obtain an oracle separating PP from PSPACE, thus solving an open problem proposed by Angluin in [An,80]. From the relativized separations to obtain absolute separations for counting complexity classes with log-time bounded computation time.Postprint (published version
