24 research outputs found
Regular Boardgames
We propose a new General Game Playing (GGP) language called Regular
Boardgames (RBG), which is based on the theory of regular languages. The
objective of RBG is to join key properties as expressiveness, efficiency, and
naturalness of the description in one GGP formalism, compensating certain
drawbacks of the existing languages. This often makes RBG more suitable for
various research and practical developments in GGP. While dedicated mostly for
describing board games, RBG is universal for the class of all finite
deterministic turn-based games with perfect information. We establish
foundations of RBG, and analyze it theoretically and experimentally, focusing
on the efficiency of reasoning. Regular Boardgames is the first GGP language
that allows efficient encoding and playing games with complex rules and with
large branching factor (e.g.\ amazons, arimaa, large chess variants, go,
international checkers, paper soccer).Comment: AAAI 201
Games, puzzles, and computation
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 147-153).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 of game as computation to a greater degree than has been done previously. I present a general family of games, called Constraint Logic, which is both mathematically simple and ideally suited for reductions to many actual board games. A deterministic version of Constraint Logic corresponds to a novel kind of logic circuit which is monotone and reversible. At the other end of the spectrum, I show that a multiplayer version of Constraint Logic is undecidable. That there are undecidable games using finite physical resources is philosophically important, and raises issues related to the Church-Turing thesis. In the second half of this thesis, I apply the Constraint Logic formalism to many actual games and puzzles, providing new hardness proofs. These applications include sliding-block puzzles, sliding-coin puzzles, plank puzzles, hinged polygon dissections, Amazons, Kohane, Cross Purposes, Tip over, and others.(cont.) Some of these have been well-known open problems for some time. For other games, including Minesweeper, the Warehouseman's Problem, Sokoban, and Rush Hour, I either strengthen existing results, or provide new, simpler hardness proofs than the original proofs.by Robert Aubrey Hearn.Ph.D
Hardness of Games and Graph Sampling
The work presented in this document is divided into two parts. The �rst part presents the hardness of games and
the second part presents Graph sampling. Non-deterministic constraint logic[1] is used to prove the hardness of
games. The games which are considered in this work is Reversi (2 player bounded game), Peg Solitaire (single
player bounded game), Badland (single player bounded game). It also contains a theoretical study of peg
solitaire on special graph classes. Reversi is proved to be PSPACE-Complete using Bounded 2CL, Peg Solitaire
is proved to be NP-Complete using Bounded NCL. Badland is proved to be NP-Complete by a reduction from
3-SAT. The objective of study of peg solitaire of special graph classes is to �nd the maximum number of marbles
we can remove from a fully �lled board, if the player is given the privilege to remove a marble from any cell
initially, then following the rules after the initial move.
The second part of the work is dedicated to graph sampling. Given a graph G, we try to sample a represen-
tative subgraph Gs which is similar to the original graph G. The properties that are being studied are Degree
Distribution, Clustering Coefficient, Average Shortest Path Length, Largest Connected Component Size. To
measure the similarity between the original graph and sample we use the metrics Kolmogorov - Smirnov test
and Kullback - Leibler divergence test. Tightly Induced Edge Sampling performs well on general graphs but
it's performance decreases when the graph is a tree. Overall TIBFS and KARGER produces a sample which
closely matches the distribution of original graphs.
On the PSPACE-completeness of Peg Duotaire and other Peg-Jumping Games
Peg Duotaire is a two-player version of the classical puzzle called Peg Solitaire. Players take turns making peg-jumping moves, and the first player which is left without available moves loses the game. Peg Duotaire has been studied from a combinatorial point of view and two versions of the game have been considered, namely the single- and the multi-hop variant. On the other hand, understanding the computational complexity of the game is explicitly mentioned as an open problem in the literature. We close this problem and prove that both versions of the game are PSPACE-complete. We also prove the PSPACE-completeness of other peg-jumping games where two players control pegs of different colors