6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs (Fall '14)

Prof. Erik Demaine     TAs: Sarah Eisenstat, Jayson Lynch


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[+] NP & PSPACE Video Games. Base PSPACE-complete problems: QSAT, Schaefer, planar Q3SAT, planar 1-in-3 Q3SAT. Viglietta metatheorems: location traversal, single-use paths, tokens, toll roads, pressure plates, buttons, doors. Applications to video games: Pac Man, FPSs (Doom, Quake, Heretic, Hexen), RPGs (Eye of the Beholder), adventure games (SCUMM), platformers (Prince of Persia, Sonic the Hedgehog, The Lost Vikings, Tomb Raider, Zelda II, Donkey Kong Country 1, 2, 3, Super Mario Bros., Lemmings) [Scribe Notes] [src]

Back to fun hardness of video games! We'll prove a bunch of “metatheorems”: video games with a few basic features are NP-hard or PSPACE-hard. Then we'll apply these metatheorems to prove NP-hardness of Boulderdash, Lode Runner, Zelda II, and Pac Man; and PSPACE-hardness of FPSs (e.g. Doom), RPGs (e.g. Eye of the Beholder), adventure games (e.g. SCUMM), Prince of Persia, Legend of Zelda: A Link to the Past, Donkey Kong Country 1, 2, and 3, and Lemmings.

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Handwritten notes, page 1/4[previous page][next page][PDF]

Handwritten notes, page 1/4[previous page][next page][PDF]

Slides, page 1/33[previous page][next page][PDF]

http://​giovanniviglietta.com/​papers/​gaming2.pdf

Slides, page 1/33[previous page][next page][PDF]

The video above should play if your web browser supports either modern Flash or HTML5 video with H.264 or WebM codec. The handwritten notes and slides should advance automatically. If you have any trouble with playback, email Erik.