How to Correctly Prune Tropical Trees

We present tropical games, a generalization of combinatorial min-max games based on tropical algebras. Our model breaks the traditional symmetry of rational zero-sum games where players have exactly opposed goals (min vs. max), is more widely applicable than min-max and also supports a form of pruning, despite it being less effective than -. Actually, min-max games may be seen as particular cases where both the game and its dual are tropical: when the dual of a tropical game is also tropical, the power of - is completely recovered. We formally develop the model and prove that the tropical pruning strategy is correct, then conclude by showing how the problem of approximated parsing can be modeled as a tropical game, profiting from pruning. Key words: combinatorial game, search, alpha-beta pruning, rational game, tropical algebra, tropical game, term, rewriting, logic, parsing

• Type: Conference
• Year: 2010
• Where: AISC
• Authors: Jean-Vincent Loddo, Luca Saiu
• Keywords: AISC 2010, Artificial Intelligence, Min-max Games, Tropical Algebra, Tropical Game