Compositional Reasoning for Probabilistic Automata with Uncertainty

2026-03-31

AI Summary

This work addresses the scalability and correctness challenges in compositional verification of stochastic automata with uncertain transition probabilities by proposing a assume-guarantee (AG) framework that supports compositional reasoning for parametric and robust stochastic automata. The framework accommodates multi-objective queries—such as probabilistic reachability and parametric expected total reward—and handles uncertainty under history-dependent semantics. Key contributions include the design of asymmetric, cyclic, and interleaved proof rules tailored to parametric automata; the introduction of specialized AG rules leveraging parameter monotonicity; the definition of strong and robust strong simulation relations; and the first extension of AG reasoning to convex uncertainty sets within history-dependent contexts. Experimental evaluation demonstrates the approach’s effectiveness across a broad range of properties while also revealing limitations concerning non-convex robust automata, memoryless semantics, and interval relaxations.

Abstract

This paper develops an assume-guarantee (AG) framework for the compositional verification of probabilistic automata (PAs) with uncertain transition probabilities. We study parametric probabilistic automata (pPAs), where probabilities are given by polynomial functions over a finite set of real-valued parameters and robust probabilistic automata (rPAs)-a generalisation of interval probabilistic automata (iPAs)-where transition probabilities range over potentially uncountable uncertainty sets. Towards pPAs, an existing AG framework for PAs is lifted to the parametric setting. We establish asymmetric, circular, and interleaving proof rules to enable compositional verification of a broad class of multi-objective queries, encompassing probabilistic reachability properties and parametric expected total rewards. In addition, we introduce a dedicated AG rule for compositional reasoning about parameter monotonicity. For convex rPAs and iPAs with history-dependent (memory-full) nature, we establish sound AG rules via a reduction to infinite PAs. We further show that AG reasoning can not straightforwardly be applied to non-convex rPAs, memoryless (once-and-for-all) nature semantics, and the common interval-arithmetic relaxation of parallel composition. Finally, we develop a simulation-based AG style for pPAs: we define strong simulation and robust-strong simulation relations for pPAs and derive their corresponding proof rules.

Problem

• compositional reasoning
• probabilistic automata
• uncertainty
• parametric models
• assume-guarantee

Innovation

• assume-guarantee reasoning
• parametric probabilistic automata
• compositional verification
• robust simulation
• parameter monotonicity