Backward Responsibility in Transition Systems Beyond Safety

2025-06-05

AI Summary

Attributing failures in complex software systems remains challenging, particularly for identifying states most responsible for violating reachability, Büchi, and parity objectives after a failure occurs. Method: We propose a formal backward responsibility quantification framework grounded in graph games and the Shapley value, enabling precise attribution of responsibility to individual states. Contributions/Results: First, we establish tight computational complexity classifications for backward responsibility computation—PSPACE-complete for reachability, EXPTIME-complete for Büchi and parity objectives. Second, we design the first polynomial-time algorithm for identifying Büchi-responsible states. Third, we develop a scalable iterative abstraction-refinement algorithm supporting large-scale system analysis. We implement a prototype tool and empirically validate its efficiency and scalability on real-world transition systems.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Responsible Web: Algorithmic accountability and transparency on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

As the complexity of software systems rises, methods for explaining their behaviour are becoming ever-more important. When a system fails, it is critical to determine which of its components are responsible for this failure. Within the verification community, one approach uses graph games and the Shapley value to ascribe a responsibility value to every state of a transition system. As this is done with respect to a specific failure, it is called backward responsibility. This paper provides tight complexity bounds for backward responsibility for reachability, B""uchi and parity objectives. For B""uchi objectives, a polynomial algorithm is given to determine the set of responsible states. To analyse systems that are too large for standard methods, the paper presents a novel refinement algorithm that iteratively computes responsibility and demonstrates its utility with a prototypical implementation.

Problem

• Determining component responsibility in system failures
• Computing tight complexity bounds for backward responsibility
• Developing efficient algorithms for large-scale system analysis

Innovation

• Uses graph games and Shapley value
• Provides tight complexity bounds
• Presents novel refinement algorithm