6.5440 Algorithmic Lower Bounds: Fun with Hardness Proofs (Fall 2023)

Prof. Erik Demaine       TAs: Josh Brunner, Lily Chung, Jenny Diomidova


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[+] Nondeterministic Constraint Logic (NCL). Constraint graph, AND/SPLIT vertex, OR vertex, protected OR vertex, CHOICE vertex, red-blue conversion, wire terminators, crossovers, grid graphs. Constraint Graph Satisfaction is NP-complete, NCL is PSPACE-complete. Reconfiguration 3SAT, sliding-block puzzles, sliding tokens, Rush Hour, hinged dissection, Sokoban, Push-2F, rolling-block mazes, plank puzzles (River Crossing), dynamic map labeling, partial searchlight scheduling.

This lecture is about Constraint Logic. We saw the basic model in Lecture 1 to prove Rush Hour is PSPACE-complete. Now we'll see the details of how Nondeterministic Constraint Logic (NCL) works, why it's PSPACE-complete, and how we can reduce to a very small gadget set: planar graphs with just AND and protected OR vertices. Then we'll apply NCL to prove PSPACE-completeness proofs for several different puzzles and problems:

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Handwritten notes, page 1/8[previous page][next page][PDF]

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http://erikdemaine.org/papers/GPC/

Slides, page 1/54[previous page][next page][PDF]