13 research outputs found
Comparing Transition Systems with Independence and Asynchronous Transition Systems
Transition systems with independence and asynchronous transition systems are noninterleaving models for concurrency arising from the same simple idea of decorating transitions with events. They differ for the choice of a derived versus a primitive notion of event which induces considerable differences and makes the two models suitable for different purposes. This opens the problem of investigating their mutual relationships, to which this paper gives a fully comprehensive answer. In details, we characterise the category of extensional asynchronous transitions systems as the largest full subcategory of the category of (labelled) asynchronous transition systems which admits , the category of transition systems with independence, as a coreflective subcategory. In addition, we introduce event-maximal asynchronous transitions systems and we show that their category is equivalent to , so providing an exhaustive characterisation of transition systems with independence in terms of asynchronous transition systems
Коалгебраическое исследование бисимуляционных паралельных процессов
The aim of this paper is to extend of coalgebra semantic and categorical methods to noninterleaving models, in particular, transition systems
with independence and labelled event structure
КОАЛГЕБРАИЧЕСКОЕ ИССЛЕДОВАНИЕ БИСИМУЛЯЦИОННЫХ\ud ПАРАЛЛЕЛЬНЫХ ПРОЦЕССОВ
The aim of this paper is to extend of coalgebra semantic and categorical methods to noninterleaving models, in particular, transition systems\ud
with independence and labelled event structure
Formal Relationships Between Geometrical and Classical Models for Concurrency
A wide variety of models for concurrent programs has been proposed during the
past decades, each one focusing on various aspects of computations: trace
equivalence, causality between events, conflicts and schedules due to resource
accesses, etc. More recently, models with a geometrical flavor have been
introduced, based on the notion of cubical set. These models are very rich and
expressive since they can represent commutation between any bunch of events,
thus generalizing the principle of true concurrency. While they seem to be very
promising - because they make possible the use of techniques from algebraic
topology in order to study concurrent computations - they have not yet been
precisely related to the previous models, and the purpose of this paper is to
fill this gap. In particular, we describe an adjunction between Petri nets and
cubical sets which extends the previously known adjunction between Petri nets
and asynchronous transition systems by Nielsen and Winskel
Relationships between Models for Concurrency
Models for concurrency can be classified with respect to three relevant parameters: behaviour/system, interleaving/noninterleaving, linear/branching time. When modelling a process, a choice concerning such parameters corresponds to choosing the level of abstraction of the resulting semantics. The classifications are formalized through the medium of category theory
Directed Homotopy in Non-Positively Curved Spaces
A semantics of concurrent programs can be given using precubical sets, in
order to study (higher) commutations between the actions, thus encoding the
"geometry" of the space of possible executions of the program. Here, we study
the particular case of programs using only mutexes, which are the most widely
used synchronization primitive. We show that in this case, the resulting
programs have non-positive curvature, a notion that we introduce and study here
for precubical sets, and can be thought of as an algebraic analogue of the
well-known one for metric spaces. Using this it, as well as categorical
rewriting techniques, we are then able to show that directed and non-directed
homotopy coincide for directed paths in these precubical sets. Finally, we
study the geometric realization of precubical sets in metric spaces, to show
that our conditions on precubical sets actually coincide with those for metric
spaces. Since the category of metric spaces is not cocomplete, we are lead to
work with generalized metric spaces and study some of their properties
Diagrammatic Algebra: from Linear to Concurrent Systems
We introduce the resource calculus, a string diagrammatic language for concurrent systems. Significantly, it
uses the same syntax and operational semantics as the signal flow calculus — an algebraic formalism for signal
flow graphs, which is a combinatorial model of computation of interest in control theory. Indeed, our approach
stems from the simple but fruitful observation that, by replacing real numbers (modelling signals) with natural
numbers (modelling resources) in the operational semantics, concurrent behaviour patterns emerge.
The resource calculus is canonical: we equip it and its stateful extension with equational theories that
characterise the underlying space of definable behaviours—a convex algebraic universe of additive relations—
via isomorphisms of categories. Finally, we demonstrate that our calculus is sufficiently expressive to capture
behaviour definable by classical Petri net