How to Correctly Prune Tropical Trees

Abstract

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 α − β. 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 α − β 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.

This work is partially financed by Marie Curie action n. 29849 Websicola and ANR-06-JCJC-0122.