Related papers: Relating coalgebraic notions of bisimulation
The analysis of concurrent and reactive systems is based to a large degree on various notions of process equivalence, ranging, on the so-called linear-time/branching-time spectrum, from fine-grained equivalences such as strong bisimilarity…
Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebras for an endofunctor on some full subcategory of the…
Simulations and bisimulations are ubiquitous in the study of concurrent systems and modal logics of various types. Besides classical relational transition systems, relevant system types include, for instance, probabilistic, weighted,…
We generalize the work by Soboci\'nski on relational presheaves and their connection with weak (bi)simulation for labelled transistion systems to a coalgebraic setting. We show that the coalgebraic notion of saturation studied in our…
This paper studies fundamental questions concerning category-theoretic models of induction and recursion. We are concerned with the relationship between well-founded and recursive coalgebras for an endofunctor. For monomorphism preserving…
We introduce and study bisimulations for coalgebras on Stone spaces [14]. Our notion of bisimulation is sound and complete for behavioural equivalence, and generalizes Vietoris bisimulations [4]. The main result of our paper is that…
A bialgebra is a structure which is simultaneously an algebra and a coalgebra, such that the algebraic and coalgebraic parts are "compatible". Bialgebras are normally studied over a field or commutative ring. In this paper, we show how to…
It is well known that the theory of coalgebras provides an abstract definition of behavioural equivalence that coincides with strong bisimulation across a wide variety of state-based systems. Unfortunately, the theory in the presence of…
In this paper the notion of bisimulation relation for linear input-state-output systems is extended to general linear differential-algebraic (DAE) systems. Geometric control theory is used to derive a linear-algebraic characterization of…
Binary multirelations generalise binary relations by associating elements of a set to its subsets. We study the structure and algebra of multirelations under the operations of union, intersection, sequential and parallel composition, as…
While behavioural equivalences among systems of the same type, such as Park/Milner bisimilarity of labelled transition systems, are an established notion, a systematic treatment of relationships between systems of different type is…
Every endofunctor of the category of classes is proved to be set-based in the sense of Aczel and Mendler, therefore, it has a final coalgebra. Other basic properties of these endofunctors are proved, e.g. the existence of a free completely…
In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon…
We investigate how various forms of bisimulation can be characterised using the technology of logical relations. The approach taken is that each form of bisimulation corresponds to an algebraic structure derived from a transition system,…
We define a notion of Lambda-simulation for coalgebraic modal logics, parametric on the choice Lambda of predicate liftings for a functor T. We show this notion is adequate in several ways: i) it preserves truth of positive formulas, ii)…
This paper introduces a new behavioral system model with distinct external and internal signals possibly evolving on different time scales. This allows to capture abstraction processes or signal aggregation in the context of control and…
We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory,…
Functor coalgebras capture a wide range of transition systems that must however evolve in discrete steps. We introduce graded coalgebras of graded monads and propose them to model continuous-time transition systems. We develop the theory of…
Co-simulation consists of the theory and techniques to enable global simulation of a coupled system via the composition of simulators. Despite the large number of applications and growing interest in the challenges, the field remains…
The aim of this paper is to introduce an algebraic structure on the set of all coalgebras with the same state space over the given type which allows us to present definitions of weak and delay bisimulation for coalgebras. Additionally, we…