10 research outputs found
An exercise on transition systems
Labelled transition systems admit different but equivalent characterizations either as relational structures or coalgebras for the powerset functor, each of them with their own merits. Notions of simulation and bisimulation, for example, are expressed in the pointfree relational calculus in a very concise and precise way. On the other hand, the coalgebraic perspective regards processes as inhabitants of a final universe and allows for an intuitive definition of the semantics of process’ combinators.
This paper is an exercise on such a dual characterisation. In particular, it discusses how a notion of weak bisimilarity can be lifted from the relational to the coalgebraic level, to become an effective reasoning tool on coinductively defined process algebras.(undefined
On coalgebras with internal moves
In the first part of the paper we recall the coalgebraic approach to handling
the so-called invisible transitions that appear in different state-based
systems semantics. We claim that these transitions are always part of the unit
of a certain monad. Hence, coalgebras with internal moves are exactly
coalgebras over a monadic type. The rest of the paper is devoted to supporting
our claim by studying two important behavioural equivalences for state-based
systems with internal moves, namely: weak bisimulation and trace semantics.
We continue our research on weak bisimulations for coalgebras over order
enriched monads. The key notions used in this paper and proposed by us in our
previous work are the notions of an order saturation monad and a saturator. A
saturator operator can be intuitively understood as a reflexive, transitive
closure operator. There are two approaches towards defining saturators for
coalgebras with internal moves. Here, we give necessary conditions for them to
yield the same notion of weak bisimulation.
Finally, we propose a definition of trace semantics for coalgebras with
silent moves via a uniform fixed point operator. We compare strong and weak
bisimilation together with trace semantics for coalgebras with internal steps.Comment: Article: 23 pages, Appendix: 3 page
Abstract Congruence Criteria for Weak Bisimilarity
We introduce three general compositionality criteria over operational
semantics and prove that, when all three are satisfied together, they guarantee
weak bisimulation being a congruence. Our work is founded upon Turi and
Plotkin's mathematical operational semantics and the coalgebraic approach to
weak bisimulation by Brengos. We demonstrate each criterion with various
examples of success and failure and establish a formal connection with the
simply WB cool rule format of Bloom and van Glabbeek. In addition, we show that
the three criteria induce lax models in the sense of Bonchi et al
Weak bisimulation for coalgebras over order enriched monads
The paper introduces the notion of a weak bisimulation for coalgebras whose
type is a monad satisfying some extra properties. In the first part of the
paper we argue that systems with silent moves should be modelled
coalgebraically as coalgebras whose type is a monad. We show that the visible
and invisible part of the functor can be handled internally inside a monadic
structure. In the second part we introduce the notion of an ordered saturation
monad, study its properties, and show that it allows us to present two
approaches towards defining weak bisimulation for coalgebras and compare them.
We support the framework presented in this paper by two main examples of
models: labelled transition systems and simple Segala systems.Comment: 44 page
A companion to coalgebraic weak bisimulation for action-type systems
We propose a coalgebraic definition of weak bisimulation for classes of coalgebras obtained from bifunctors in the category Set. Weak bisim-ilarity for a system is obtained as strong bisimilarity of a transformed system. The particular transformation consists of two steps: First, the behavior on actions is lifted to behavior on finite words. Second, the behavior on finite words is taken modulo the hiding of internal or in-visible actions, yielding behavior on equivalence classes of words closed under silent steps. The coalgebraic definition is validated by two cor-respondence results: one for the classical notion of weak bisimulation of Milner, another for the notion of weak bisimulation for generative probabilistic transition systems as advocated by Baier and Hermanns.
Towards weak bisimulation for coalgebras
SIGLEAvailable from TIB Hannover: RR 7739(02-11) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman
Towards weak bisimulation for coalgebras
SIGLEAvailable from TIB Hannover: RR 7739(02-11) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman
Towards Weak Bisimulation For Coalgebras
This report contains a novel approach to observation equivalence for coalgebras