▁of ▁input ▁variables ▁before ▁generating ▁graphs . ▁Z DD s ▁automatically ▁suppress ▁the ▁variables ▁for ▁objects ▁which ▁never ▁appear ▁in ▁combination , ▁hence ▁the ▁efficiency ▁for ▁manip ulating ▁sparse ▁combinations . ▁ ▁Another ▁advantage ▁of ▁Z DD s ▁is ▁that ▁the ▁number ▁of ▁ 1 - paths ▁in ▁the ▁graph ▁is ▁exactly ▁equal ▁to ▁the ▁number ▁of ▁elements ▁in ▁the ▁combination ▁set . ▁In ▁original ▁B DD s , ▁the ▁node ▁elim ination ▁breaks ▁this ▁property . ▁Therefore , ▁Z DD s ▁are ▁better ▁than ▁simple ▁B DD s ▁to ▁represent ▁combination ▁sets . ▁It ▁is , ▁however , ▁better ▁to ▁use ▁the ▁original ▁B DD s ▁when ▁representing ▁ordinary ▁Boolean ▁functions , ▁as ▁shown ▁in ▁Figure ▁ 7 . ▁ ▁Basic ▁Oper ations ▁Here ▁we ▁have ▁the ▁basic ▁operations ▁for ▁Z DD s , ▁as ▁they ▁are ▁slightly ▁different ▁from ▁those ▁of ▁the ▁original ▁B DD s . ▁One ▁may ▁refer ▁to ▁Figure ▁ 8 ▁for ▁examples ▁generated ▁from ▁the ▁table ▁below . ▁ ▁Em pty () ▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ <0x09> returns ▁ ø ▁( empty ▁set ) ▁Base () <0x09> <0x09> <0x09> returns { 0 } ▁Sub set 1 ( P , ▁var ) <0x09> ▁▁▁▁▁▁▁ ▁returns ▁the ▁subset ▁of ▁P ▁such ▁as ▁var ▁= ▁ 1 ▁ ▁Sub set 0 ( P , ▁var ) <0x09> ▁▁▁▁▁▁▁ ▁returns ▁the ▁subset ▁of ▁P ▁such ▁as ▁var ▁= ▁ 0 ▁Change ( P , ▁var ) <0x09> ▁▁▁▁▁▁▁ ▁returns ▁P ▁when ▁var ▁is ▁invert ed ▁Union ( P , ▁Q ) <0x09> <0x09> returns