AG rules for fairness and general quantitative objectives in convex robust PAs

Develop assume-guarantee proof rules for convex robust probabilistic automata with history-dependent nature that cover fairness assumptions and general quantitative objectives beyond safety multi-objective queries, ensuring that fairness is preserved under the reduction to probabilistic automata and is compatible with the convexity-preserving parallel composition operator.

Background

In Section 6, the paper establishes assume-guarantee rules for convex robust probabilistic automata (rPAs) with history-dependent nature, but restricts the results to safety multi-objective queries. The soundness relies on a reduction from convex rPAs to (possibly uncountably branching) probabilistic automata and a convexity-preserving parallel composition.

The authors note that extending these results to fairness assumptions and more general quantitative objectives would require additional care to preserve fairness properties through the reduction, and explicitly defer this extension.