A Formally Verified IEEE 754 Floating-Point Implementation of Interval Iteration for MDPs
arXiv:2501.10127 · doi:10.1007/978-3-031-98679-6_6
Abstract
We present an efficiently executable, formally verified implementation of interval iteration for MDPs. Our correctness proofs span the entire development from the high-level abstract semantics of MDPs to a low-level implementation in LLVM that is based on floating-point arithmetic. We use the Isabelle/HOL proof assistant to verify convergence of our abstract definition of interval iteration and employ step-wise refinement to derive an efficient implementation in LLVM code. To that end, we extend the Isabelle Refinement Framework with support for reasoning about floating-point arithmetic and directed rounding modes. We experimentally demonstrate that the verified implementation is competitive with state-of-the-art tools for MDPs, while providing formal guarantees on the correctness of the results.