Linguistic Geometry - From Search to Construction (Operations Research/Computer Science Interfaces Series)

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Linguistic Geometry: From Search to Construction is the first book of its kind. Linguistic Geometry (LG) is an approach to the construction of mathematical models for large-scale multi-agent systems. A number of such systems, including air/space combat, robotic manufacturing, software re-engineering and Internet cyberwar, can be modeled as abstract board games. These are games with moves that can be represented by the movement of abstract pieces over locations on an abstract board. The purpose of LG is to provide strategies to guide the games' participants to their goals. Traditionally, discovering such strategies required searches in giant game trees. These searches are often beyond the capacity of modern and even conceivable future computers.
LG dramatically reduces the size of the search trees, making the problems computationally tractable. LG provides a formalization and abstraction of search heuristics used by advanced experts including chess grandmasters. Essentially, these heuristics replace search with the construction of strategies. To formalize the heuristics, LG employs the theory of formal languages (i.e. formal linguistics), as well as certain geometric structures over an abstract board. The new formal strategies solve problems from different domains far beyond the areas envisioned by the experts. For a number of these domains, Linguistic Geometry yields optimal solutions.

Linguistic Geometry - From Search to Construction (Operations Research/Computer Science Interfaces Series) Review

Linguistic Geometry: From Search to Construction is a remarkable book. It offers hope to solve large complex problems where conventional methods provide solutions that are computationally intractable. The problems in question cover a large area: from military strategies to robot control on the factory floor. As long as the problem may be represented as a kind of a game, where the game pieces move in a real or imaginary multi-dimensional board, using rules expressible via geometrical relations on the board, the Linguistic Geometry (LG) method would cover it. It is interesting to note that while the adversarial pieces are needed for the game model, the notion of the adversary may not be even defined for the original problem. Indeed, as demonstrated in the example of creating repair schedule for the power plants from the book, the adversary may be artificially introduced. Of course, for many problems, such as finding a winning strategy on a battlefield for Air, Ground, or Undersea operations, etc., the friendly and adversarial pieces, game boards and other gaming elements are usually already in place. Thus, the LG methodology would be clearly applicable. Entertainment games would be another such example. The method for finding the winning strategies described in the book is quite ingenious. It originally stems from the heuristics that the Chess grand masters employ to defeat their opponents. The book author, Boris Stilman, spent quite a few years with the longest reigning world Chess champion, Michael Botvinnik, distilling Botvinnik's ideas about how the grandmasters win or loose games, into an elegant mathematical theory which later became the Linguistic Geometry. The book has both theory and plenty of easy as well as medium difficulty examples. If you were interested in the kind of problems mentioned above, it would be worthwhile for you to read the book. For me, it was entertaining as well.

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