Abstraction-Refinement for Hierarchical Probabilistic Models

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 hierarchical structure repetitive parts. This not only occurs naturally in robotics, but also programs describing, e.g., network protocols. Such often repeatedly call subroutine similar In paper, we focus on local case, which subroutines have limited effect overall system state. The key ideas accelerate analysis such (1) treat behavior as uncertain remove uncertainty detailed if needed, (2) abstract into parametric template, then analyse template. These two embedded an abstraction-refinement loop that analyses MDPs. A prototypical implementation shows efficacy approach.