Solving computational tasks on finite topologies by means of relation algebra and the RelView tool

We present a relation-algebraic approach to solve computational tasks concerning finite topologies. It is based on the modeling of finite topologies via relations and the specification of the notions in question by relation-algebraic expressions and formulae. The latter then are evaluated with the help of the BDD-based specific purpose computer algebra system RelView after a simple translation into the system's programming language. We apply the technique to different problems and show how the solutions behave with regard to running time if implemented and evaluated by RelView. Experiments with RelView led to a new result on minimal subbases for finite topologies, that is proved at the end of the paper.