A Matrix-Oriented View of Bisimulation Quotients over Dioid-Labeled Transition Systems

This work considers a special type of bisimulations between transition systems labeled with elements drawn from a dioid. In contrast to the traditional approach, all edges of the systems under consideration bear unique edge labels. Bisimulations between such systems are defined via 0-1-matrices and share some properties with common bisimulations. A particular focus is on bisimulation equivalences and their induced quotients where we show some observations regarding linear equations, eigenvectors, and eigenvalues.