. The aim of this paper is to investigate the relation between two models of concurrent systems: tile rewrite systems and coalgebras. Tiles are rewrite rules with side effects which are endowed with operations of parallel and sequential composition and synchronization. Their models can be described as monoidal double categories. Coalgebras can be considered, in a suitable mathematical setting, as dual to algebras. They can be used as models of dynamical systems with hidden states in order to study concepts of observational equivalence and bisimilarity in a more general setting. In order to capture in the coalgebraic presentation the algebraic structure given by the composition operations on tiles, coalgebras have to be endowed with an algebraic structure as well. This leads to the concept of structured coalgebras, i.e., coalgebras for an endofunctor on a category of algebras. However, structured coalgebras are more restrictive than tile models. Those models which can be presented as st...

In this report we study the connection between two well known models for interactive systems. Reactive Systems à la Leifer and Milner allow to derive an interactive semantics from a reduction semantics guaranteeing, semantics (bisimilarity). Universal Coalgebra provides a categorical framework where bisimilarity can be characterized as final semantics, i.e., as the unique morphism to the final coalgebra. Moreover, if lifting a coalgebra to a structured setting is possible, then bisimilarity is compositional with respect to the lifted structure. Here we show that for every reactive system we can build a coalgebra. Furthermore, if bisimilarity is compositional in the reactive system, then we can lift this coalgebra to a structured coalgebra. 1

In this report we study the connection between two well known models for interactive systems. Reactive Systems à la Leifer and Milner allow to derive an interactive semantics from a reduction semantics guaranteeing, semantics (bisimilarity). Universal Coalgebra provides a categorical framework where bisimilarity can be characterized as final semantics, i.e., as the unique morphism to the final coalgebra. Moreover, if lifting a coalgebra to a structured setting is possible, then bisimilarity is compositional with respect to the lifted structure. Here we show that for every reactive system we can build a coalgebra. Furthermore, if bisimilarity is compositional in the reactive system, then we can lift this coalgebra to a structured coalgebra.

The semantics of process calculi has traditionally been specified by labelled transition systems (ltss), but with the development of name calculi it turned out that reaction rules (i.e., unlabelled transition rules) are often more natural. This leads to the question of how behavioural equivalences (bisimilarity, trace equivalence, etc.) defined for lts can be transferred to unlabelled transition systems. Recently, in order to answer this question, several proposals have been made with the aim of automatically deriving an lts from reaction rules in such a way that the resulting equivalences are congruences. Furthermore these equivalences should agree with the standard semantics, whenever one exists. In this paper we propose saturated semantics, based on a weaker notion of observation and orthogonal to all the previous proposals, and we demonstrate the appropriateness of our semantics by means of two examples: logic programming and open Petri nets. We also show that saturated semantics can be efficiently characterized through the so called semi-saturated games. Finally, we provide coalgebraic models relying on presheaves.