1 research outputs found
Walking Through Doors Is Hard, Even Without Staircases: Proving PSPACE-Hardness via Planar Assemblies of Door Gadgets
A door gadget has two states and three tunnels that can be traversed by an
agent (player, robot, etc.): the "open" and "close" tunnel sets the gadget's
state to open and closed, respectively, while the "traverse" tunnel can be
traversed if and only if the door is in the open state. We prove that it is
PSPACE-complete to decide whether an agent can move from one location to
another through a planar assembly of such door gadgets, removing the
traditional need for crossover gadgets and thereby simplifying past
PSPACE-hardness proofs of Lemmings and Nintendo games Super Mario Bros., Legend
of Zelda, and Donkey Kong Country. Our result holds in all but one of the
possible local planar embedding of the open, close, and traverse tunnels within
a door gadget; in the one remaining case, we prove NP-hardness.
We also introduce and analyze a simpler type of door gadget, called the
self-closing door. This gadget has two states and only two tunnels, similar to
the "open" and "traverse" tunnels of doors, except that traversing the traverse
tunnel also closes the door. In a variant called the symmetric self-closing
door, the "open" tunnel can be traversed if and only if the door is closed. We
prove that it is PSPACE-complete to decide whether an agent can move from one
location to another through a planar assembly of either type of self-closing
door. Then we apply this framework to prove new PSPACE-hardness results for
eight different 3D Mario games and Sokobond.Comment: Accepted to FUN2020, 35 pages, 41 figure