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

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

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

4. Constraint Graphs Machine state = orientation constraint graph

5. Constraint Logic = 1 = 2 Rule: at least 2 units incoming at a vertex 11 2 Move: reverse an edge, preserving Rule

6. AND vertex Rule: at least 2 units incoming at a vertex 11 11 2 TT TF FFTT not your usual AND gate! inputs output

7. SPLIT vertex Rule: at least 2 units incoming at a vertex 11 1 2 FF FT TTF outputs input

8. OR vertex Rule: at least 2 units incoming at a vertex 22 22 2 TT TF FFTT not your usual OR gate! inputs output T

9. Decision Problem can you reverse this edge?

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

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

12. Sliding-Block Puzzles 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 OR 1 2 AND wants red OR wants blue

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

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

18. Boolean Formulas

19. Quantified Boolean Formulas (QBF) xxyywwzz

20. Existential Quantifier

21. Universal Quantifier

22. Latch A B lockedun

23. Universal Quantifier

24. Crossover Gadget

25. OR from Protector OR

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

27. Triangular Rush 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] bounded unbounded 0 players (simulation) 1 player (puzzle) 2 players (game) team, imperfect info PSPACE EXPTIME P Undecidable NEXPTIME PSPACE NP PSPACE

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

34. Amazons [Hearn 2005] fanout