# Strategy Representation by Decision Trees with Linear Classifiers

## TL;DR

This paper introduces decision trees with linear classifiers for representing strategies in graph games and MDPs, achieving more efficient strategy representations than standard decision trees, with experimental validation.

## Contribution

The paper proposes a novel decision tree with linear classifiers for strategy representation in graph games and MDPs, improving efficiency over traditional decision trees.

## Key findings

- More efficient strategy representations compared to standard decision trees
- Implementation and experimental validation on graph games and MDPs
- Significant reduction in complexity of strategy data structures

## Abstract

Graph games and Markov decision processes (MDPs) are standard models in reactive synthesis and verification of probabilistic systems with nondeterminism. The class of $\omega$-regular winning conditions; e.g., safety, reachability, liveness, parity conditions; provides a robust and expressive specification formalism for properties that arise in analysis of reactive systems. The resolutions of nondeterminism in games and MDPs are represented as strategies, and we consider succinct representation of such strategies. The decision-tree data structure from machine learning retains the flavor of decisions of strategies and allows entropy-based minimization to obtain succinct trees. However, in contrast to traditional machine-learning problems where small errors are allowed, for winning strategies in graph games and MDPs no error is allowed, and the decision tree must represent the entire strategy. In this work we propose decision trees with linear classifiers for representation of strategies in graph games and MDPs. We have implemented strategy representation using this data structure and we present experimental results for problems on graph games and MDPs, which show that this new data structure presents a much more efficient strategy representation as compared to standard decision trees.