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Bisimulation from Open Maps
 Information and Computation
, 1994
"... An abstract definition of bisimulation is presented. It enables a uniform definition of bisimulation across a range of different models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction f ..."
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Cited by 116 (42 self)
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An abstract definition of bisimulation is presented. It enables a uniform definition of bisimulation across a range of different models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction from Petri nets) and labelled event structures are considered. On transition systems the abstract definition readily specialises to Milner's strong bisimulation. On event structures it explains and leads to a revision of historypreserving bisimulation of Rabinovitch and Traktenbrot, Goltz and van Glabeek. A tieup with open maps in a (pre)topos, as they appear in the work of Joyal and Moerdijk, brings to light a promising new model, presheaves on categories of pomsets, into which the usual category of labelled event structures embeds fully and faithfully. As an indication of its promise, this new presheaf model has "refinement" operators, though further work is required to justify their appropriateness and understand their relation to previous attempts. The general approach yields a logic, generalising HennessyMilner logic, which is characteristic for the generalised notion of bisimulation.
Bisimulation and Open Maps
 In Proc. LICS'93, Eighth Annual Symposium on Logic in Computer Science
, 1993
"... An abstract definition of bisimulation is presented. It enables a uniform definition of bisimulation across a range of different models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction from ..."
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Cited by 36 (7 self)
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An abstract definition of bisimulation is presented. It enables a uniform definition of bisimulation across a range of different models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction from Petri nets) and labelled event structures are considered. On transition systems the abstract definition readily specialises to Milner's strong bisimulation. On event structures it explains and leads to a revision of historypreserving bisimulation of Rabinovitch and Traktenbrot, Goltz and van Glabeek. A tieup with open maps in a (pre)topos, as they appear in the work of Joyal and Moerdijk, brings to light a promising new model, presheaves on categories of pomsets, into which the usual category of labelled event structures embeds fully and faithfully. As an indication of its promise, this new presheaf model has "refinement" operators, though further work is required to justify their appropri...
Petri Nets and Bisimulations
 THEORETICAL COMPUTER SCIENCE
, 1995
"... Several categorical relationships (adjunctions) between models for concurrency have been established, allowing the translation of concepts and properties from one model to another. A central example is a coreflection between Petri nets and asynchronous transition systems. The purpose of the pres ..."
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Cited by 16 (7 self)
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Several categorical relationships (adjunctions) between models for concurrency have been established, allowing the translation of concepts and properties from one model to another. A central example is a coreflection between Petri nets and asynchronous transition systems. The purpose of the present paper is to illustrate the use of such relationships by transferring to Petri nets a general concept of bisimulation.
On The Specification Of Concurrent Systems
, 1991
"... In models of concurrent processes constraints on the order of events are often represented by partial orders, and schedules of events are then defined using an algebra of standard operations such as sequential and parallel composition. In this dissertation the notion of partial order is replaced by ..."
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Cited by 9 (0 self)
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In models of concurrent processes constraints on the order of events are often represented by partial orders, and schedules of events are then defined using an algebra of standard operations such as sequential and parallel composition. In this dissertation the notion of partial order is replaced by that of a set with a metric which takes values in a given ordered monoid. Partial orders are the simple case of a monoid whose two elements represent the presence or absence of a constraint. An ordered monoid can be seen as a monoidal category, and schedules based on it are categories enriched in the monoid. Algebraic operations on schedules can then be defined as constructions in the category of schedules. These definitions rely on certain properties of a category of schedules, such as closure and completeness. To simplify proofs of these properties, two constructions are defined. The first creates a category of unlabeled schedules from a system of constraints. The second adds labels to unl...
Categories in Concurrency
 Semantics and Logics of Computation, Publications of the Newton Institute
, 1997
"... These notes survey a range of models for parallel computation, including interleaving models like transition systems, synchronisation trees and languages (often called Hoare traces in this context), and models like asynchronous transition systems, event structures, pomsets and Mazurkiewicz traces wh ..."
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Cited by 5 (0 self)
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These notes survey a range of models for parallel computation, including interleaving models like transition systems, synchronisation trees and languages (often called Hoare traces in this context), and models like asynchronous transition systems, event structures, pomsets and Mazurkiewicz traces where concurrency is represented more explicitly by a form of causal independence. The presentation is unified by casting the models in a categorytheoretic framework. One aim is to use category theory to provide abstract characterisations of constructions like parallel composition valid throughout a range of different models and to provide formal means for translating between different models. The framework helps in extending the useful concept of bisimulation equivalence from its familiar situation on transition systems, to independence models where without a careful analysis even the appropriate definition of bisimulation is not clearcut. 1 Contents 1 Introduction 3 2 Transition systems 5...
Equivalence semantics for concurrency: comparison and application
, 1998
"... Since the development of CCS and other process algebras, many extensions to these process algebras have been proposed to model different aspects of concurrent computation. It is important both theoretically and practically to understand the relationships between these process algebras and between ..."
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Cited by 3 (2 self)
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Since the development of CCS and other process algebras, many extensions to these process algebras have been proposed to model different aspects of concurrent computation. It is important both theoretically and practically to understand the relationships between these process algebras and between the semantic equivalences that are defined for them. In this thesis, I investigate the comparison of semantic equivalences based on bisimulation which are defined for process algebras whose behaviours are described by structured operational semantics, and expressed as labelled transition systems. I first consider a hierarchy of bisimulations for extensions to CCS, using both existing and new results to describe the relationships between their equivalences with respect to pure CCS terms. I then consider a more general approach to comparison by investigating labelled transition systems with structured labels. I define bisimulation homomorphisms between labelled transition systems with different labels, and show how these can be used to compare equivalences. Next, I work in the metatheory of process algebras and consider a new format that is an extension of the tyft/tyxt format for transition system specifications. This format treats labels syntactically instead of schematically, and hence I use a definition of bisimulation which requires equivalence between labels instead of exact matching. I show that standard results such as congruence and conservative extension hold for the new format. I then investigate how comparison of equivalences can be approached through the notion of extension to transition system specifications. This leads to the main results of this study which show how in a very general fashion the bisimulations defined for two different process algebras can be compared over a subset of terms of the process algebras. I also consider what implications the conditions which are required to obtain these results have for modelling process algebras, and show that these conditions do not impose significant limitations. Finally, I show how these results can be applied to existing process algebras. I model a number of process algebras with the extended format and derive new results from the metatheory developed. ii
Convenient Category of Processes and Simulations I: Modulo Strong Bisimilarity
, 1995
"... Deep categorical analyses of various aspects of concurrency have been developed, but a uniform categorical treatment of the very first concepts seems to be hindered by the fact that the existing representations of processes as bisimilarity classes do not provide a sufficient account of computational ..."
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Cited by 1 (1 self)
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Deep categorical analyses of various aspects of concurrency have been developed, but a uniform categorical treatment of the very first concepts seems to be hindered by the fact that the existing representations of processes as bisimilarity classes do not provide a sufficient account of computational morphisms. In the present paper, we describe a category of processes modulo strong bisimulations, with the bisimilarity preserving simulations as morphisms, and show that it is isomorphic to  and can be conveniently represented by  a subcategory of transition systems, with graph morphisms. The representative of each process and every morphism can effectively calculated, using coinduction (but with no reference to proper classes). The method is applicable to richer notions of a process as well, which are studied in the sequel. 1 Introduction A process is usually presented as some kind of a labelled graph. In fact, any directed graph with labelled edges and a distinguished initial node...
Towards a Categorical Axiomatics of Bisimulation
, 1999
"... We give an axiomatic category theoretic account of bisimulation in process algebras based on the idea of functional bisimulations as open maps. The axiomatisation centres on 2monads, T , on Cat. Operations on processes, such as nondeterministic sum, prefixing and parallel composition are modelled u ..."
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We give an axiomatic category theoretic account of bisimulation in process algebras based on the idea of functional bisimulations as open maps. The axiomatisation centres on 2monads, T , on Cat. Operations on processes, such as nondeterministic sum, prefixing and parallel composition are modelled using functors in the Kleisli category for the 2monad T . We may define the notion of open map for any such 2monad; in examples of interest, the definition agrees exactly with the usual notion of functional bisimulation. Under a condition on T , namely that it be a dense KZmonad, which we define, it follows that functors in Kl(T ) preserve open maps, i.e., they respect functional bisimulation. We further investigate structures on Kl(T ) that exist for axiomatic reasons, primarily because T is a dense KZmonad, and we study how those structures help to model operations on processes. We outline how this analysis gives ideas for modelling higher order processes. We conclude by making compariso...