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26
Relations in Concurrency
"... The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the seman ..."
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Cited by 263 (33 self)
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The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the semantics of nondeterministic dataflow. Profunctors are shown to play a key role in relating models for concurrency and to support an interpretation as higherorder processes (where input and output may be processes). Two recent directions of research are described. One is concerned with a language and computational interpretation for profunctors. This addresses the duality between input and output in profunctors. The other is to investigate general spans of event structures (the spans can be viewed as special profunctors) to give causal semantics to higherorder processes. For this it is useful to generalise event structures to allow events which “persist.”
Towards a Mathematical Operational Semantics
 In Proc. 12 th LICS Conf
, 1997
"... We present a categorical theory of `wellbehaved' operational semantics which aims at complementing the established theory of domains and denotational semantics to form a coherent whole. It is shown that, if the operational rules of a programming language can be modelled as a natural transformation ..."
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Cited by 134 (9 self)
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We present a categorical theory of `wellbehaved' operational semantics which aims at complementing the established theory of domains and denotational semantics to form a coherent whole. It is shown that, if the operational rules of a programming language can be modelled as a natural transformation of a suitable general form, depending on functorial notions of syntax and behaviour, then one gets both an operational model and a canonical, internally fully abstract denotational model for free; moreover, both models satisfy the operational rules. The theory is based on distributive laws and bialgebras; it specialises to the known classes of wellbehaved rules for structural operational semantics, such as GSOS.
On the Foundations of Final Coalgebra Semantics: nonwellfounded sets, partial orders, metric spaces
, 1998
"... ..."
A Logical View Of Concurrent Constraint Programming
, 1995
"... . Concurrent Constraint Programming (CCP) has been the subject of growing interest as the focus of a new paradigm for concurrent computation. Like logic programming it claims close relations to logic. In fact CCP languages are logics in a certain sense that we make precise in this paper. In recent ..."
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Cited by 23 (4 self)
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. Concurrent Constraint Programming (CCP) has been the subject of growing interest as the focus of a new paradigm for concurrent computation. Like logic programming it claims close relations to logic. In fact CCP languages are logics in a certain sense that we make precise in this paper. In recent work it was shown that the denotational semantics of determinate concurrent constraint programming languages forms a fibred categorical structure called a hyperdoctrine, which is used as the basis of the categorical formulation of firstorder logic. What this shows is that the combinators of determinate CCP can be viewed as logical connectives. In this paper we extend these ideas to the operational semantics of such languages and thus make available similar analogies for a much broader variety of languages including indeterminate CCP languages and concurrent blockstructured imperative languages. CR Classification: F3.1, F3.2, D1.3, D3.3 Key words: Concurrent constraint programming, simula...
Open Maps, Behavioural Equivalences, and Congruences
, 1996
"... Spans of open maps have been proposed by Joyal, Nielsen, and Winskel as a way of adjoining an abstract equivalence, Pbisimilarity, to a category of models of computation M, where P is an arbitrary subcategory of observations. Part of the motivation was to recast and generalise Milner's wellkno ..."
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Cited by 15 (0 self)
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Spans of open maps have been proposed by Joyal, Nielsen, and Winskel as a way of adjoining an abstract equivalence, Pbisimilarity, to a category of models of computation M, where P is an arbitrary subcategory of observations. Part of the motivation was to recast and generalise Milner's wellknown strong bisimulation in this categorical setting. An issue
A Coalgebraic Foundation for Linear Time Semantics
 In Category Theory and Computer Science
, 1999
"... We present a coalgebraic approach to trace equivalence semantics based on lifting behaviour endofunctors for deterministic action to Kleisli categories of monads for nondeterministic choice. In Set , this gives a category with ordinary transition systems as objects and with morphisms characterised ..."
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Cited by 14 (1 self)
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We present a coalgebraic approach to trace equivalence semantics based on lifting behaviour endofunctors for deterministic action to Kleisli categories of monads for nondeterministic choice. In Set , this gives a category with ordinary transition systems as objects and with morphisms characterised in terms of a linear notion of bisimulation. The final object in this category is the canonical abstract model for trace equivalence and can be obtained by extending the final coalgebra of the deterministic action behaviour to the Kleisli category of the nonempty powerset monad. The corresponding final coalgebra semantics is fully abstract with respect to trace equivalence.
Open Maps (at) Work
 DEPARTMENT OF COMPUTER SCIENCE, UNIVERSITY OF AARHUS
, 1995
"... The notion of bisimilarity, as defined by Park and Milner, has turned out to be one of the most fundamental notions of operational equivalences in the field of process algebras. Not only does it induce a congruence (largest bisimulation) in CCS which have nice equational properties, it has also ..."
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Cited by 9 (3 self)
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The notion of bisimilarity, as defined by Park and Milner, has turned out to be one of the most fundamental notions of operational equivalences in the field of process algebras. Not only does it induce a congruence (largest bisimulation) in CCS which have nice equational properties, it has also proven itself applicable for numerous models of parallel computation and settings such as Petri Nets and semantics of functional languages. In an attempt to understand the relationships and differences between the extensive amount of research within the field, Joyal, Nielsen, and Winskel recently presented an abstract categorytheoretic definition of bisimulation. They identify spans of morphisms satisfying certain "path lifting" properties, socalled open maps, as a possible abstract definition of bisimilarity. In [JNW93] they show, that they can capture Park and Milner's bisimulation. The aim of this paper is to show that the abstract definition of bisimilarity is applicable "in practice" by showing how a representative selection of wellknown bisimulations and equivalences, such as e.g. Hennessy's testing equivalence, Milner and Sangiorgi's barbed bisimulation, and Larsen and Skou's probabilistic bisimulation, are captured in the setting of open maps and hence, that the proposed notion of open maps seems successful. Hence, we confirm that the treatment of strong bisimulation in [JNW93] is not a oneoff application of open maps.
SProc Categorically
 in: Proceedings CONCUR'94 (SpringerVerlag
, 1994
"... . We provide a systematic reconstruction of Abramsky's category SProc of synchronous processes [Abr93]: SProc is isomorphic to a span category on a category of traces. The significance of the work is twofold: It shows that the original presentation of SProc in mixed formulations is unnecessary ..."
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Cited by 7 (2 self)
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. We provide a systematic reconstruction of Abramsky's category SProc of synchronous processes [Abr93]: SProc is isomorphic to a span category on a category of traces. The significance of the work is twofold: It shows that the original presentation of SProc in mixed formulations is unnecessary  a simple categorical description exists. Furthermore, the techniques employed in the reconstruction suggest a general method of obtaining process categories with structure similar to SProc. In particular, the method of obtaining bisimulation equivalence in our setting, which represents an extension of the work of Joyal, Nielsen and Winskel [JNW93], has natural application in many settings. 1 Introduction In [Abr93], Abramsky proposed a new paradigm for the semantics of computation, interaction categories, where the following substitutions are made: Denotational semantics Categories Interaction categories Domains objects Interface specifications Continuous functions maps Commun...
New Bisimulation Semantics for Distributed Systems
, 2007
"... Bisimulation semantics are a very pleasant way to define the semantics of systems, mainly because the simplicity of their definitions and their nice coalgebraic properties. However, they also have some disadvantages: they are based on a sequential operational semantics defined by means of an ordinar ..."
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Cited by 7 (0 self)
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Bisimulation semantics are a very pleasant way to define the semantics of systems, mainly because the simplicity of their definitions and their nice coalgebraic properties. However, they also have some disadvantages: they are based on a sequential operational semantics defined by means of an ordinary transition system, and in order to be bisimilar two systems have to be âtoo similarâ. In this work we will present several natural proposals to define weaker bisimulation semantics that we think properly capture the desired behaviour of distributed systems. The main virtue of all these semantics is that they are real bisimulation semantics, thus inheriting most of the good properties of bisimulation semantics. This is so because they can be defined as particular instances of Jacobs and Hughesâ categorical definition of simulation, which they have already proved to satisfy all those properties.
Petri Nets, Traces, and Local Model Checking
 Proceedings of the 4th International Conference on Algebraic Methodology and Software Technology, Lecture Notes in Computer Science 936, SpringerVerlag
, 1995
"... It has been observed that the behavioural view of concurrent systems that all possible sequences of actions are relevant is too generous; Not all sequences should be considered as likely behaviours. By taking progress fairness assumptions into account one obtains a more realistic behavioural view of ..."
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Cited by 5 (0 self)
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It has been observed that the behavioural view of concurrent systems that all possible sequences of actions are relevant is too generous; Not all sequences should be considered as likely behaviours. By taking progress fairness assumptions into account one obtains a more realistic behavioural view of the systems. In this paper we consider the problem of performing model checking relative to this behavioural view. We present a CTLlike logic which is interpreted over the model of concurrent systems labeled 1safe nets. It turns out that Mazurkiewicz trace theory provides a useful setting in which the progress fairness assumptions can be formalized in a natural way. We provide the first, to our knowledge, set of sound and complete tableau rules for a CTLlike logic interpreted under progress fairness assumptions. keywords: fair progress, labeled 1safe nets, local model checking, maximal traces, partial orders, inevitability 1 Introduction Recently attention has focused on behavioural v...