Implementation of Polyhedral Operations in CORA 2024

Tool presentation: Polyhedra are a common set representation with widespread appli- cations in many areas of research, including convex geometry, reachability analysis, and invariant set computation. Their popularity stems from a tight relation to linear program- ming. Apart from some basic set operations with analytic formulae, the implementation of many polyhedral set operations in tools is not well documented. For this reason, we describe the evaluation of common set operations on polyhedra, including their runtime complexity, and provide an overview of their implementation as a dedicated class in the MATLAB tool Continuous Reachability Analyzer (CORA) for set-based computing. In particular, we highlight the handling of unbounded and degenerate sets. Finally, we com- pare our implementation to the popular multi-parametric toolbox.