A toolchain for strategy synthesis with spatial properties

We present an application of strategy synthesis to enforce spatial properties. This is achieved by implementing a toolchain that enables the tools \texttt{CATLib} and \texttt{VoxLogicA} to interact in a fully automated way. The Contract Automata Library (\texttt{CATLib}) is aimed at both composition and strategy synthesis of games modelled in a dialect of finite state automata. The Voxel-based Logical Analyser (\texttt{VoxLogicA}) is a spatial model checker for the verification of properties expressed using the Spatial Logic of Closure Spaces on pixels of digital images. We provide examples of strategy synthesis on automata encoding motion of agents in spaces represented by images, as well as a proof-of-concept realistic example based on a case study from the railway domain. The strategies are synthesised with \texttt{CAT\-Lib}, while the properties to enforce are defined by means of spatial model checking of the images with \texttt{VoxLogicA}. The combination of spatial model checking with strategy synthesis provides a toolchain for checking and enforcing mobility properties in multi-agent systems in which location plays an important role, like in many collective adaptive systems. We discuss the toolchain's performance also considering several recent improvements.