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

## Prof. Erik Demaine     TAs: Sarah Eisenstat, Jayson Lynch

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 [+] 0- and 2-player games. 0-player games: Conway's Game of Life is undecidable, Deterministic Constraint Logic (DCL) is PSPACE-complete. Bounded 2-player games are PSPACE-complete: impartial/partizan game/avoid/seek SAT, Kayles, Geography, Reversi/Othello, bounded 2-player Constraint Logic (2CL). [Scribe Notes] [src] We've proved hardness of a lot of puzzles, which can be viewed as 1-player games — the player represents the nondeterminism in move choices. This lecture is about games involving fewer or more players. Zero-player games are essentially simulations, like a regular computer. The prototypical example here is Conway's Game of Life, which is PSPACE-complete or undecidable depending on whether you bound the board. A more modern example is Deterministic Constraint Logic, a version of constraint logic where edge-reversal order is deterministically defined (but many edges reverse in parallel), which is still PSPACE-complete. In multiplayer games, we want to know whether a player (say, the first) has a winning strategy. In the worst case, all other players collude as a single entity, so the game reduces to two players. Thus we obtain 2-player games. We'll see many typical starting points for proving hardness of 2-player games, from QSAT itself to impartial/partizan game/seek/avoid SAT (from another amazing Schaefer paper). PSPACE-hard 2-player graph games include Kayles (essentially 2-player independent set), Geography (essentially 2-player longest path), Reversi/Othello, and bounded 2-player Constraint Logic (2CL).
 No support for video detected. Install Flash or use an HTML5 browser. Download Video: 360p, 720p Handwritten notes, page 1/6 • [previous page] • [next page] • [PDF] Handwritten notes, page 1/6 • [previous page] • [next page] • [PDF] Slides, page 1/39 • [previous page] • [next page] • [PDF] Slide from Lecture 1. http://​erikdemaine.org/​papers/​GPC/​ Slides, page 1/39 • [previous page] • [next page] • [PDF]

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