1 / 34

Complexity of Games & Puzzles [Demaine, Hearn & many others]

Complexity of Games & Puzzles [Demaine, Hearn & many others] Rengo Kriegspiel? unbounded EXPTIME Undecidable PSPACE PSPACE bridge? bounded NP PSPACE P NEXPTIME team, imperfect info 0 players (simulation) 1 player (puzzle) 2 players (game) Constraint Logic [Hearn & Demaine 2009]

victoria
Download Presentation

Complexity of Games & Puzzles [Demaine, Hearn & many others]

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Complexity of Games & Puzzles[Demaine, Hearn & many others] Rengo Kriegspiel? unbounded EXPTIME Undecidable PSPACE PSPACE bridge? bounded NP PSPACE P NEXPTIME team,imperfect info 0 players (simulation) 1 player (puzzle) 2 players (game)

  2. Constraint Logic[Hearn & Demaine 2009] unbounded EXPTIME Undecidable PSPACE PSPACE bounded PSPACE NP P NEXPTIME team,imperfect info 0 players (simulation) 1 player (puzzle) 2 players (game)

  3. Constraint Graphs Machine = graph,red & blue edges

  4. Constraint Graphs Machine state = orientation constraint graph

  5. Constraint Logic = 1 1 1 = 2 2 Rule: at least 2 unitsincoming at a vertex Move: reverse an edge, preserving Rule

  6. AND vertex T F T F T T inputs 1 1 1 1 2 output F T Rule: at least 2 unitsincoming at a vertex not your usualAND gate!

  7. SPLIT vertex T T F F F outputs 1 1 1 2 input T F Rule: at least 2 unitsincoming at a vertex

  8. OR vertex T F F T T T inputs 2 2 2 2 2 output T F T Rule: at least 2 unitsincoming at a vertex not your usualOR gate!

  9. Decision Problem can you reverse this edge?

  10. Constraint Logic[Hearn & Demaine 2009] unbounded EXPTIME Undecidable PSPACE PSPACE bounded PSPACE NP P NEXPTIME team,imperfect info 0 players (simulation) 1 player (puzzle) 2 players (game)

  11. Decision Problem can you reverse this edge? Theorem: PSPACE-complete

  12. Sliding-BlockPuzzles http://www.cs.brandeis.edu/~storer/JimPuzzles/ZPAGES/zzzDadsPuzzler.html

  13. Sliding-Block Puzzles[Hearn & Demaine 2002] Corollary: PSPACE-complete

  14. Sliding-Block Puzzles[Hearn & Demaine 2002] Corollary: PSPACE-complete

  15. Wiring Vertices Together AND 1 AND wants red OR wants blue 2 OR

  16. Red-Blue Conversion assume an even number of conversions

  17. Red-Blue Conversion assume an even number of conversions

  18. BooleanFormulas

  19. Quantified Boolean Formulas (QBF) x x y y w w z z

  20. Existential Quantifier

  21. Universal Quantifier

  22. Latch A un locked B

  23. Universal Quantifier

  24. Crossover Gadget

  25. OR fromProtector OR

  26. Rush Hour[Hearn & Demaine 2002] PSPACE-completeness known [Flake & Baum 2002]

  27. TriangularRush Hour [Hearn & Demaine 2009]

  28. Open: 1×1 Rush Hour[Tromp & Cilibrasi 2008] • P or PSPACE-complete or …?

  29. Plank Puzzles [Hearn 2004]

  30. Sokoban[Hearn & Demaine 2002] PSPACE-completeness known [Culberson 1998]

  31. Push-2F[Demaine, Hearn, Hoffmann 2002]

  32. Constraint Logic[Hearn & Demaine 2009] unbounded EXPTIME Undecidable PSPACE PSPACE bounded PSPACE NP P NEXPTIME team,imperfect info 0 players (simulation) 1 player (puzzle) 2 players (game)

  33. Constraint Logic[Hearn & Demaine 2009] unbounded EXPTIME Undecidable PSPACE PSPACE bounded PSPACE NP P NEXPTIME team,imperfect info 0 players (simulation) 1 player (puzzle) 2 players (game)

  34. Amazons[Hearn 2005] fanout

More Related