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We present a nondeterministic model of computation based on reversing edge directions in weighted directed graphs with minimum inflow constraints on vertices. Deciding whether this simple graph model can be manipulated in order to reverse the direction of a particular edge is shown to be PSPACE-complete by a reduction from Quantified Boolean Formulas. We… (More)

There is a fundamental connection between the notions of game and of computation. At its most basic level, this is implied by any game complexity result, but the connection is deeper than this. One example is the concept of alternating nondeterminism, which is intimately connected with two-player games. In the first half of this thesis, I develop the idea… (More)

We present a nondeterministic model of computation based on reversing edge directions in weighted directed graphs with minimum inflow constraints on vertices. Deciding whether this simple graph model can be manipulated in order to reverse the direction of a particular edge is shown to be PSPACE-complete by a reduction from Quantified Boolean Formulas. We… (More)

We introduce a simple game family, called Constraint Logic, where players reverse edges in a directed graph while satisfying vertex inflow constraints. This game family can be interpreted in many different game-theoretic settings , ranging from zero-player automata to a more economic setting of team multiplayer games with hidden information. Each setting… (More)

We prove PSPACE-completeness of a class of pushing-block puzzles similar to the classic Sokoban, extending several previous results [1, 5, 12]. The puzzles consist of unit square blocks on an integer lattice; some of the blocks are movable. The robot may move horizontally and vertically in order to reach a specified goal position. The puzzle variants differ… (More)

We show several natural questions about hinged dissec-tions of polygons to be PSPACE-hard. The most basic of these is: Given a hinged set of pieces and two configurations for them, can we swing the pieces on the hinges to transform one configuration to the other? We also consider variants in which the configurations must be convex, the placement of hinges… (More)

Amazons is a board game which combines elements of Chess and Go. It has become popular in recent years, and has served as a useful platform for both game-theoretic study and AI games research. Buro [2] showed that simple Amazons endgames are NP-equivalent, leaving the complexity of the general case as an open problem. We settle this problem, by showing that… (More)

Learning to perform via reinforcement typically requires extensive search through an intractably large space of possible behaviors. In the brain, reinforcement learning is hypothesized to be carried out in large measure by the basal ganglia / striatal complex (Schultz 2000; Granger 2005), a phylogenet-ically old set of structures that dominate the brains of… (More)

- Kyle Burke, Erik D. Demaine, Harrison Gregg, Robert A. Hearn, Adam Hesterberg, Michael Hoffmann +9 others
- ArXiv
- 2015

We study the computational complexity of the Buttons & Scissors game and obtain sharp thresholds with respect to several parameters. Specifically we show that the game is NP-complete for C = 2 colors but polytime solvable for C = 1. Similarly the game is NP-complete if every color is used by at most F = 4 buttons but polytime solvable for F ≤ 3. We also… (More)