Compositional Reasoning for Parametric Probabilistic Automata

2025-06-10

AI Summary

Scalability of multi-objective verification for parametric probabilistic automata (pPAs)—particularly involving parametric probabilistic properties and expected total rewards—remains severely limited. Method: This paper introduces the first compositional assume-guarantee (AG) reasoning framework for pPAs, proposing three novel AG proof rules: asymmetric, cyclic, and interleaved. It further establishes the first compositional monotonicity reasoning rule for pPAs, enabling modeling of inter-component parameter dependencies. The approach integrates AG reasoning, parametric model checking, multi-objective probabilistic logics (e.g., PCTL+R), and monotonicity analysis. Results: Experiments demonstrate that the framework efficiently verifies a broad class of multi-objective queries, significantly improving scalability and interpretability—especially under uncertainty and high parameter sensitivity—while preserving verification precision.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Multiagent Systems: Multiagent Systems under Uncertainty
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We establish an assume-guarantee (AG) framework for compositional reasoning about multi-objective queries in parametric probabilistic automata (pPA) - an extension to probabilistic automata (PA), where transition probabilities are functions over a finite set of parameters. We lift an existing framework for PA to the pPA setting, incorporating asymmetric, circular, and interleaving proof rules. Our approach enables the verification of a broad spectrum of multi-objective queries for pPA, encompassing probabilistic properties and (parametric) expected total rewards. Additionally, we introduce a rule for reasoning about monotonicity in composed pPAs.

Problem

• Extends assume-guarantee framework to parametric probabilistic automata
• Enables verification of multi-objective queries in pPA
• Introduces rules for monotonicity in composed parametric automata

Innovation

• Assume-guarantee framework for pPA
• Multi-objective query verification
• Monotonicity rule for composed pPAs