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A mathematical formulation to efficiently determine "life status" in the game of Go

The game of Go is an ancient board game. In this game, players aim to capture the stones of their opponent by enclosing them. One possible condition for a stone is described as "safe". A safe stone can never be captured. This has been represented with a static determination by Benson [1]. In this paper, we analyze this determination mathematically, using the BW graph model that was introduced by Sato et al. [2][3][4][5]. As the result, we propose a new representation that reduces the required number of backtracking searches.