Collaborating Authors

The Game of Hex: An Automatic Theorem Proving Approach to Game Programming

AAAI Conferences

The game of Hex is a two-player game with simple rules, a deep underlying mathematical beauty, and a strategic complexity comparable to that of Chess and Go. The massive game-tree search techniques developed mostly for Chess, and successfully used for Checkers, Othello, and a number of other games, become less useful for games with large branching factors like Go and Hex. We offer a new approach, which results in superior playing strength. This approach emphasizes deep analysis of relatively few game positions. In order to reach this goal, we develop an automatic theorem proving technique for topological analysis of Hex positions. We also discuss in detail an idea of modeling Hex positions with electrical resistor circuits. We explain how this approach is implemented in Hexy - the strongest known Hex-playing computer program, able to compete with best human players.

Artificial Intelligence Game Talk, University of Alberta, Hex and Chess


U of Alberta created the first Computing Science department in Canada in 1964. It has a long tradition of research in AI (is rated 3rd in the world in machine learning). It has also led in the development of AI for strategy games. The results can be commercialized in non-game applications as well. Among these are Checkers, Chess, Go and Poker, The evening's talks were by Jonathan Schaeffer (computer chess) and Ryan Hayward (the strategy game Hex).

Temperature Discovery Search

AAAI Conferences

Temperature Discovery Search (TDS) is a new minimaxbased game tree search method designed to compute or approximate the temperature of a combinatorial game. TDS is based on the concept of an enriched environment, where a combinatorial game G is embedded in an environment consisting of a large set of simple games of decreasing temperature. Optimal play starts in the environment, but eventually must switch to G. TDS finds the temperature of G by determining when this switch must happen. Both exact and heuristic versions of TDS are described and evaluated experimentally. In experiments with sum games in Amazons, TDS outperforms an αβ searcher.

Elwyn Berlekamp, game theorist and coding pioneer, dies at 78

UC Berkeley EECS

Elwyn Berlekamp, a UC Berkeley mathematician and game theorist whose error-correcting codes allowed spacecraft from Voyager to the Hubble Space Telescope to send accurate, detailed and beautiful images back to Earth, died April 9 at his home in Piedmont, California, from complications of pulmonary fibrosis. A professor emeritus of mathematics and of electrical engineering and computer sciences, Berlekamp was 78. Berlekamp was a "genius" in many areas, according to colleague Richard Karp, a UC Berkeley professor emeritus of electrical engineering and computer sciences and holder of computer science's premier honor, the Turing Award. "He was a brilliant person who was always effective in everything he tried to do, whether it was mathematics or game theory or consulting and investment. He had a curious and powerful mind," said Karp, who was the first chair of UC Berkeley's computer sciences division upon its creation and merger with electrical engineering in 1973.