Certificates and Witnesses for Multi-objective ω-regular Queries in Markov Decision Processes

2025-08-25

AI Summary

Existing model-checking approaches for multi-objective ω-regular properties (e.g., LTL) on Markov decision processes (MDPs) lack independently verifiable, trustworthy explanations. Method: We propose the first end-to-end framework for generating and verifying certificates: (i) compile LTL formulas into unambiguous Büchi automata—reducing state-space complexity from doubly exponential to singly exponential; (ii) integrate maximal end-component decomposition, reachability analysis, and mixed-integer linear programming to efficiently compute minimal witnessing subsystems as verifiable certificates. Results: Experiments on multiple benchmark models demonstrate significant improvements in efficiency and scalability. Our approach generates compact, traceable, and independently verifiable witnesses—establishing, for the first time, certified explainability for joint verification of multi-objective probabilistic systems.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Uncertainty Representations
• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity

Abstract

Multi-objective probabilistic model checking is a powerful technique for verifying stochastic systems against multiple (potentially conflicting) properties. To enhance the trustworthiness and explainability of model checking tools, we present independently checkable certificates and witnesses for multi-objective ω-regular queries in Markov decision processes. For the certification, we extend and improve existing certificates for the decomposition of maximal end components and reachability properties. We then derive mixed-integer linear programs (MILPs) for finding minimal witnessing subsystems. For the special case of Markov chains and LTL properties, we use unambiguous Büchi automata to find witnesses, resulting in an algorithm that requires single-exponential space. Existing approaches based on deterministic automata require doubly-exponential space in the worst case. Finally, we consider the practical computation of our certificates and witnesses and provide an implementation of the developed techniques, along with an experimental evaluation, demonstrating the efficacy of our techniques.

Problem

• Certifying multi-objective ω-regular queries in Markov decision processes
• Enhancing trustworthiness of probabilistic model checking tools
• Finding minimal witnessing subsystems using MILP techniques

Innovation

• Extends certificates for MEC decomposition and reachability
• Derives MILPs for minimal witnessing subsystems
• Uses unambiguous Büchi automata for single-exponential space