Abstract

Graph games played by two players over finite-state graphs are central in many problems in computer science. In particular, graph games with \(\omega \)-regular winning conditions, specified as parity objectives, which can express properties such as safety, liveness, fairness, are the basic framework for verification and synthesis of reactive systems. The decisions for a player at various states of the graph game are represented as strategies. While the algorithmic problem for solving graph games with parity objectives has been widely studied, the most prominent data-structure for strategy representation in graph games has been binary decision diagrams (BDDs). However, due to the bit-level representation, BDDs do not retain the inherent flavor of the decisions of strategies, and are notoriously hard to minimize to obtain succinct representation. In this work we propose decision trees for strategy representation in graph games. Decision trees retain the flavor of decisions of strategies and allow entropy-based minimization to obtain succinct trees. However, decision trees work in settings (e.g., probabilistic models) where errors are allowed, and overfitting of data is typically avoided. In contrast, for strategies in graph games no error is allowed, and the decision tree must represent the entire strategy. We develop new techniques to extend decision trees to overcome the above obstacles, while retaining the entropy-based techniques to obtain succinct trees. We have implemented our techniques to extend the existing decision tree solvers. We present experimental results for problems in reactive synthesis to show that decision trees provide a much more efficient data-structure for strategy representation as compared to BDDs.

Highlights

  • We extend existing decision tree solvers with our techniques and present experimental results to demonstrate the effectiveness of our approach in reactive synthesis

  • In this work we propose decision trees for strategy representation in graph games

  • While decision trees have been used in probabilistic settings where errors are allowed and overfitting of data is avoided, for graph games, strategies must be entirely represented without errors

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Summary

Introduction

The synthesis problem for reactive systems asks for the construction of a winning strategy in the corresponding graph game. The algorithmic problem asks for a given graph game with a parity objective and a starting state, whether player 1 has a winning strategy. This problem is central in verification and synthesis. We have applied our implementation to compare decision trees and BDDs for representation of strategies for problems in reactive synthesis. We considered randomly generated LTL formulae, and the graph games obtained for the realizability of such formulae In both the above experiments the decision trees represent the winning strategies much more efficiently as compared to BDDs. Related work. We extend existing decision tree solvers with our techniques and present experimental results to demonstrate the effectiveness of our approach in reactive synthesis

Graph Games and Strategies
Decision Trees and Decision Tree Learning
Strategies as Training Sets and Decision Trees
Strategy-DT Learning
Heuristics
Experimental Results
AIGER specifications
Random LTL
Conclusion
A Artifact Description
B Correctness of Algorithm k-look-ahead ID3
Full Text
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