Abstraction-Refinement for Hierarchical Probabilistic Models
This addresses verification challenges in robotics and network protocols, but it is incremental as it builds on existing abstraction-refinement methods for hierarchical models.
The paper tackles the state space explosion problem in verifying hierarchical Markov decision processes by exploiting repetitive structures and using an abstraction-refinement loop with parametric templates, showing efficacy through a prototypical implementation.
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.