Abstraction-Refinement for Hierarchical Probabilistic Models

TL;DR

This paper introduces an abstraction-refinement approach for hierarchical probabilistic models, specifically Markov decision processes, to mitigate state space explosion by exploiting repetitive subroutine structures.

Contribution

It presents a novel hierarchical analysis method that abstracts similar subroutines into parametric templates and refines them only when necessary, improving efficiency.

Findings

Effective reduction in analysis complexity for hierarchical MDPs.

Prototype implementation demonstrates practical efficiency gains.

Applicable to systems with repetitive probabilistic components.

Abstract

Markov decision processes are a ubiquitous formalism for modelling systems with non-deterministic and probabilistic behavior. Verification of these models is subject to the famous state space explosion problem. We alleviate this problem by exploiting a hierarchical structure with repetitive parts. This structure not only occurs naturally in robotics, but also in probabilistic programs describing, e.g., network protocols. Such programs often repeatedly call a subroutine with similar behavior. In this paper, we focus on a local case, in which the subroutines have a limited effect on the overall system state. The key ideas to accelerate analysis of such programs are (1) to treat the behavior of the subroutine as uncertain and only remove this uncertainty by a detailed analysis if needed, and (2) to abstract similar subroutines into a parametric template, and then analyse this template. These two ideas are embedded into an abstraction-refinement loop that analyses hierarchical MDPs. A prototypical implementation shows the efficacy of the approach.