A bisimulation for a coalgebra of functor on the category sets can be described via in relations, lifted functor. final then gives rise to coinduction principle, which states that two bisimilar elements are equal. For polynomial functors, this leads well-known descriptions. In present paper we look at dual notion "apartness". Intuitively, apart if there is positive way distinguish them. Phrased...

Bisimulation-up-to enhances the bisimulation proof method for process equivalence. We present its generalization from labelled transition systems to arbitrary coalgebras, and show that for a large class of systems, enhancements such as bisimulation up to bisimilarity, up to equivalence and up to context are sound proof techniques. This allows for simplified bisimulation proofs for many differen...

The notion of bisimulation has escaped the world of continuous, and subsequently, hybrid systems. Recently, notions of bisimulation for continuous systems have been developed based on the categorical framework of Joyal, Nielsen and Winskel. In this paper, we combine known notions of bisimulation for discrete systems with recent notions for continuous systems and develop novel but natural notion...

Petri nets are a popular formalism for modeling and analyzing distributed systems. Tokens in net models can represent the control flow state or resources produced/consumed by transition firings. We define resource as part (a submultiset) of markings call two equivalent when replacing one them with another any marking does not change observable behavior. consider similarity bisimilarity, congrue...