Efficient Formally Verified Maximal End Component Decomposition for MDPs

Abstract Identifying a Markov decision process’s maximal end components is a prerequisite for applying sound probabilistic model checking algorithms. In this paper, we present the first mechanized correctness proof of a maximal end component decomposition algorithm, which is an important algorithm in model checking, using the Isabelle/HOL theorem prover. We iteratively refine the high-level algorithm and proof into an imperative LLVM bytecode implementation that we integrate into the Modest Toolset ’s existing model checker. We bring the benefits of interactive theorem proving into practice by reducing the trusted code base of a popular probabilistic model checker and we experimentally show that our new verified maximal end component decomposition in performs on par with the tool’s previous unverified implementation.