How to correctly prune tropical trees

TL;DR

This paper introduces tropical games, a generalized framework for combinatorial min-max games based on tropical algebras, enabling broader applicability and a form of pruning, with formal correctness proofs and an application to parsing.

Contribution

It develops a formal model of tropical games, proves the correctness of tropical pruning strategies, and demonstrates their application to approximated parsing.

Findings

Tropical games generalize min-max games using tropical algebra.

Tropical pruning is correct but less effective than alpha-beta.

Application to parsing shows practical utility of the model.

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 alpha-beta. 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 alpha-beta 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.