In this article, we present a concrete realisation of the ETCS hybrid level 3 concept, whose practical viability was evaluated in a field demonstration in 2017. Hybrid level 3 introduces virtual subsections as subdivisions of classical track sections with trackside train detection. Our approach introduces an add-on for the radio block centre (RBC) of Thales, called virtual block function (VBF), which computes the occupation states of the virtual subsections using the train position reports, train integrity information, and the track occupation states. From the perspective of the RBC, the VBF behaves as an interlocking that transmits all signal aspects for virtual signals introduced for each virtual subsection to the RBC. We report on the development of the VBF, implemented as a formal B model executed at runtime using ProB and successfully used in a field demonstration to control real trains. Keywords B-method • Animation • Model-based testing • Model checking • ETCS

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Abstract. We present an integration of the constraint solving kernel of the ProB model checker with the SMT solver Z3. We apply the combined solver to B and Event-B predicates, featuring higher-order datatypes and constructs like set comprehensions. To do so we rely on the finite set logic of Z3 and provide a new translation from B to Z3, better suited for constraint solving. Predicates can then be solved by the two solvers working hand in hand: constraints are set up in both solvers simultaneously and (intermediate) results are transferred. We thus combine a constraint logic programming based solver with a DPLL(T) based solver into a single procedure. The improved constraint solver finds application in many validation tasks, from animation of implicit specifications, to test case generation, bounded and symbolic model checking on to disproving of proof obligations. We conclude with an empirical evaluation of our approach focusing on two dimensions: comparing low and high-level encodings of B as well as comparing pure ProB to ProB combined with Z3.

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