Results 1  10
of
29
Towards a homotopy theory of process algebra
 2008) 353–388 (electronic). MR2426108 (2009d:68115), Zbl 1151.68037
"... Abstract. This paper proves that labelled flows are expressive enough to contain all process algebras which are a standard model for concurrency. More precisely, we construct the space of execution paths and of higher dimensional homotopies between them for every process name of every process algebr ..."
Abstract

Cited by 15 (10 self)
 Add to MetaCart
(Show Context)
Abstract. This paper proves that labelled flows are expressive enough to contain all process algebras which are a standard model for concurrency. More precisely, we construct the space of execution paths and of higher dimensional homotopies between them for every process name of every process algebra with any synchronization algebra using a notion of labelled flow. This interpretation of process algebra satisfies the paradigm of higher dimensional automata: one nondegenerate full ndimensional cube (no more no less) in the underlying space of the time flow corresponding to the concurrent execution of n actions. This result will enable us in future papers to develop an homotopical approach of process algebras. Indeed, several homological constructions related to the causal structure of time flow are possible only in the framework of flows. Contents
A category of higherdimensional automata
, 2005
"... Abstract. We show how parallel composition of higherdimensional automata (HDA) can be expressed categorically in the spirit of Winskel & Nielsen. Employing the notion of computation path introduced by van Glabbeek, we define a new notion of bisimulation of HDA using open maps. We derive a conn ..."
Abstract

Cited by 11 (3 self)
 Add to MetaCart
(Show Context)
Abstract. We show how parallel composition of higherdimensional automata (HDA) can be expressed categorically in the spirit of Winskel & Nielsen. Employing the notion of computation path introduced by van Glabbeek, we define a new notion of bisimulation of HDA using open maps. We derive a connection between computation paths and carrier sequences of dipaths and show that bisimilarity of HDA can be decided by the use of geometric techniques.
Combinatorics of labelling in higher dimensional automata
"... Abstract. The main idea for interpreting concurrent processes as labelled precubical sets is that a given set of n actions running concurrently must be assembled to a labelled ncube, in exactly one way. The main ingredient is the nonfunctorial construction called labelled directed coskeleton. It i ..."
Abstract

Cited by 11 (5 self)
 Add to MetaCart
(Show Context)
Abstract. The main idea for interpreting concurrent processes as labelled precubical sets is that a given set of n actions running concurrently must be assembled to a labelled ncube, in exactly one way. The main ingredient is the nonfunctorial construction called labelled directed coskeleton. It is defined as a subobject of the labelled coskeleton, the latter coinciding in the unlabelled case with the right adjoint to the truncation functor. This nonfunctorial construction is necessary since the labelled coskeleton functor of the category of labelled precubical sets does not fulfil the above requirement. We prove in this paper that it is possible to force the labelled coskeleton functor to be wellbehaved by working with labelled transverse symmetric precubical sets. Moreover, we prove that this solution is the only one. A transverse symmetric precubical set is a precubical set equipped with symmetry maps and with a new kind of degeneracy map called transverse degeneracy. Finally, we also prove that the two settings are equivalent from a directed algebraic topological viewpoint. To illustrate, a new semantics of CCS, equivalent to the old one, is given. Contents
Event Structures with Symmetry
 GDP FESTSCHRIFT, ENTCS, TO APPEAR
"... A category of event structures with symmetry is introduced and its categorical properties investigated. Applications to the eventstructure semantics of higher order processes, nondeterministic dataflow and the unfolding of Petri nets with multiple tokens are sketched. ..."
Abstract

Cited by 8 (5 self)
 Add to MetaCart
A category of event structures with symmetry is introduced and its categorical properties investigated. Applications to the eventstructure semantics of higher order processes, nondeterministic dataflow and the unfolding of Petri nets with multiple tokens are sketched.
Events, Causality and Symmetry
, 2008
"... The article discusses causal models, such as Petri nets and event structures, how they have been rediscovered in a wide variety of recent applications, and why they are fundamental to computer science. A discussion of their present limitations leads to their extension with symmetry. The consequences ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
The article discusses causal models, such as Petri nets and event structures, how they have been rediscovered in a wide variety of recent applications, and why they are fundamental to computer science. A discussion of their present limitations leads to their extension with symmetry. The consequences, actual and potential, are discussed.
Invariants of directed spaces
 Appl. Categ. Structures
"... URL: www.math.auc.dk/research/reports/reports.htm e ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
URL: www.math.auc.dk/research/reports/reports.htm e
Bisimulation for higherdimensional automata. A geometric interpretation. Research report R200501
 Department of Mathematical Sciences, Aalborg University
, 2005
"... We show how parallel composition of higherdimensional automata (HDA) can be expressed categorically in the spirit of Winskel & Nielsen. Employing the notion of computation path introduced by van Glabbeek, we define a new notion of bisimulation of HDA using open maps. We derive a connection betw ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
We show how parallel composition of higherdimensional automata (HDA) can be expressed categorically in the spirit of Winskel & Nielsen. Employing the notion of computation path introduced by van Glabbeek, we define a new notion of bisimulation of HDA using open maps. We derive a connection between computation paths and carrier sequences of dipaths and show that bisimilarity of HDA can be decided by the use of geometric techniques.
On the expressivity of symmetry in event structures
"... This paper establishes a bridge between presheaf models for concurrency and the more operationallyinformative world of event structures. It concentrates on a particular presheaf category, consisting of presheaves over finite partial orders of events; such presheaves form a model of nondeterministic ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
This paper establishes a bridge between presheaf models for concurrency and the more operationallyinformative world of event structures. It concentrates on a particular presheaf category, consisting of presheaves over finite partial orders of events; such presheaves form a model of nondeterministic processes in which the computation paths have the shape of partial orders. It is shown how with the introduction of symmetry event structures represent all presheaves over finite partial orders. This is in contrast with plain event structures which only represent certain separated
Formal Relationships Between Geometrical and Classical Models for Concurrency
"... Abstract. 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 fla ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
(Show Context)
Abstract. 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 number 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. 1 1