A linguistic geometry model for an arimaa bot

Up to date, the strongest computer programs in some popular games like chess use the alpha-beta search algorithm with advanced heuristics created for that particular game. In 1997, a computer defeated a chess world champion for the first time. This event inspired Omar Syed to develop a game called Arimaa. He intended to make it difficult to solve under present search approaches. Linguistic Geometry is a technique that offers a formal method based on the expertise of human chess masters, to make the development of complex heuristics easier. Linguistic Geometry works through string processing. These strings represent in-game logic structures. The processing is made through a kind of formal grammars called controlled grammars. A Linguistic Geometry based model requires a grammar for each one of the essential components of Linguistic Geometry: trajectories, zones, translations and searches. This article introduces a Linguistic Geometry based model for the game of Arimaa. The propposed model uses Linguistic Geometry's default grammar of trajectories; two grammars of zones particular to the game of Arimaa, original to this work; Linguistic Geometry's default grammar of translations with some changes; two grammars of searches, proposed in this work to be used in some tests of the proposed model. The model is tested through some test cases. These are used as input for a software implementation of the proposed model. The results given by the software are compared against the analysis made by a human player.