The Space Complexity of Pebble Games on Trees

tudy two different pebble games that are yed on directed ‘acyclic graphs. One game uses ek pebbles only. We call this game the black pebble ot me WCS black and white pebbles 1 it lack & white pebble game. Both have b,een studied in the past. For results on the ck pebble game see [I ,S,G,150]. For results on the ck &, white pebble game se% 12,4,7-91. The black pebble game is played according to the f~~~al~ing rules: (i) a pebble may be removed from a vertex at any time; (ii) if all predecessors of an unpebbled vertex v are ebbled, a pebble may be placed on v; (iii) if all predecessors of an unpebbled vertex v are ed, a pebble may be mcved from a predecessor