AG reasoning for rPAs under alternative nature semantics (Markovian and branching/merging)

Develop assume-guarantee reasoning and corresponding semantics for robust probabilistic automata under alternative nature models, including dynamic Markovian natures that depend on the path length and more general semantics that allow branching and merging of states, beyond the stepwise memoryless or history-dependent settings adopted in this work.

Background

The robust-PAs section adopts stepwise nature semantics (either memoryless or history-dependent) under state–action rectangularity. The authors point out that additional nature variants exist in the literature, such as dynamic Markovian natures or semantics with branching and merging.

They explicitly defer the treatment of these alternative semantics—together with the associated AG reasoning framework—to future work.

References

Further variants are possible, such as (dynamic) Markovian natures that additionally depend on the length of the path, or more general semantics that allow branching and merging of states. We focus on the stepwise setting with memoryless or memory-full (history-dependent) nature and leave other variants to future work.

— Compositional Reasoning for Probabilistic Automata with Uncertainty  (2603.29550 - Mertens et al., 31 Mar 2026) in Remark 6.1 (Robust probabilistic automata: nature semantics variants)