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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 in-flow 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)

- 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)

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)

- ROBERT A. HEARN
- 2006

TipOver TM is a popular puzzle in which the goal is to navigate a layout of vertical crates, tipping some over to reach others, so as to eventually reach a target crate. Crates can only tip into empty space, and you can't jump over empty space to reach other crates. The challenge is to tip the crates in the right directions and the right order. Figure 1:… (More)