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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)

- Robert A Hearn
- 2007

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 [3] showed that simple Amazons endgames are NP-equivalent, leaving the complexity of the general case as an open problem. 1 Konane is an ancient Hawaiian game,… (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)

- Rationality Ken Binmore, Todd Kaplan, Shmuel Zamir, Combinatorial Auctions, V Rakesh, Algorithmic Vohra +20 others
- 2016

Description: The ability to understand and predict behavior in strategic situations, in which an individual's success in making choices depends on the choices of others, has been the domain of game theory since the 1950s. Developing the theories at the heart of game theory has resulted in 8 Nobel Prizes and insights that researchers in many fields continue… (More)

- Robert A Hearn
- 2003

Sliding-block puzzles have long fascinated aficionados of recreational mathematics. From Sam Loyd's infamous 14-15 puzzle to the latest whimsical variants such as Rush Hour TM , these puzzles seem to offer a maximum of complexity for a minimum of space. In the usual kind of sliding-block puzzle, one is given a box containing a set of rectangular pieces, and… (More)

- Robert A Hearn
- 2001

Most Artificial Intelligence (AI) work can be characterized as either " high-level " (e.g., logical, symbolic) or " low-level " (e.g., connectionist, behavior-based robotics). Each approach suffers from particular drawbacks. High-level AI uses abstractions that often have no relation to the way real, biological brains work. Low-level AI, on the other hand,… (More)