Verified Model Checking of Timed Automata

Abstract

Abstract. We have constructed a mechanically verified prototype implementation of a model checker for timed automata, a popular formalism for modeling real-time systems. Our goal is two-fold: first, we want to provide a reference implementation that is fast enough to check other model checkers against it on reasonably sized benchmarks; second, we strive for maximal feature compatibility with the state-of-the-art tool Uppaal. The starting point of our work is an existing highly abstract formalization of reachability checking of timed automata. We reduce checking of Uppaal-style models to the problem of model checking a single automaton in this abstract formalization, while retaining the ability to perform on the fly model-checking. Using the Isabelle Refinement Framework, the abstract specification of the model checker is refined, via multiple intermediate steps, to an actual imperative implementation in Standard ML. The resulting tool is evaluated on a set of standard benchmarks to demonstrate its practical usability.

Verified Certification of Reachability Checking for Timed Automata

“…Knowledge of this data structure is not necessary to understand the rest of the paper. Thus we refer the interested reader to Bengtsson and Yi [4] and to Wimmer and Lammich [29,31] for a verification of this data structure. In the remainder we will only use the term "zones" instead of referring to their implementation as DBMs.…”

“…shared state variables, are used. However, due to the existing verified product construction for such a formalism [31], it is sufficient to study the case of a single timed automaton here.…”

“…Previous work [31] has addressed this problem by constructing a model checker for timed automata that is fully verified using Isabelle/HOL [25]. This tool is intended to be a reference implementation that can be used to scrutinize the correctness of other model checkers.…”

“…Related Work This work is based on an existing Isabelle/HOL formalization of timed automata model checking [29,31]. Other proof-assistant formalizations of timed automata focus on proving elementary properties about the basic formalism [33,34], or proving properties about concrete automata [26,10,8], but none of them are concerned with model checking.…”

QED at Large: A Survey of Engineering of Formally Verified Software

“…Another line of work in Isabelle/HOL formalizes various model checkers, for example for Linear Temporal Logic (Esparza et al, 2013) and for timed automata (Wimmer and Lammich, 2018).…”