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11
Presheaf Models for Concurrency
, 1999
"... In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their wo ..."
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Cited by 45 (19 self)
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In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their work inspired this thesis by suggesting that presheaf categories could provide abstract models for concurrency with a builtin notion of bisimulation. We show how
A Fully Abstract Presheaf Semantics of SCCS with Finite Delay
 Department of Computer Science, University of Aarhus
, 1999
"... We present a presheaf model for the observation of infinite as well as finite computations. We apply it to give a denotational semantics of SCCS with finite delay, in which the meanings of recursion are given by final coalgebras and meanings of finite delay by initial algebras of the process equatio ..."
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Cited by 19 (3 self)
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We present a presheaf model for the observation of infinite as well as finite computations. We apply it to give a denotational semantics of SCCS with finite delay, in which the meanings of recursion are given by final coalgebras and meanings of finite delay by initial algebras of the process equations for delay. This can be viewed as a first step in representing fairness in presheaf semantics. We give a concrete representation of the presheaf model as a category of generalised synchronisation trees and show that it is coreflective in a category of generalised transition systems, which are a special case of the general transition systems of Hennessy and Stirling. The open map bisimulation is shown to coincide with the extended bisimulation of Hennessy and Stirling. Finally we formulate Milners operational semantics of SCCS with finite delay in terms of generalised transition systems and prove that the presheaf semantics is fully abstract with respect to extended bisimulation
Linearity in Process Languages
"... The meaning and mathematical consequences of linearity (managing without a presumed ability to copy) are studied for a pathbased model of processes which is also amodel of affinelinear logic. This connection yields an affinelinear language for processes, automatically respecting openmap bisim ..."
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Cited by 13 (10 self)
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The meaning and mathematical consequences of linearity (managing without a presumed ability to copy) are studied for a pathbased model of processes which is also amodel of affinelinear logic. This connection yields an affinelinear language for processes, automatically respecting openmap bisimulation, in which a range of process operations can be expressed. An operational semantics isprovided for the tensor fragment of the language. Different ways to make assemblies of processes lead to differentchoices of exponential, some of which respect bisimulation.
A Linear Metalanguage for Concurrency
 Handbook of Logic in Computer Science
, 1998
"... A metalanguage for concurrent process languages is introduced. ..."
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Cited by 11 (4 self)
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A metalanguage for concurrent process languages is introduced.
Categorical Models for Concurrency: Independence, Fairness and Dataflow
 BRICS DISSERTATION SERIES DS001
, 2000
"... This thesis is concerned with formal semantics and models for concurrent computational systems, that is, systems consisting of a number of parallel computing sequential systems, interacting with each other and the environment. A formal semantics gives meaning to computational systems by describing t ..."
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Cited by 6 (4 self)
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This thesis is concerned with formal semantics and models for concurrent computational systems, that is, systems consisting of a number of parallel computing sequential systems, interacting with each other and the environment. A formal semantics gives meaning to computational systems by describing their behaviour in a mathematical model. For concurrent systems the interesting aspect of their computation is often how they interact with the environment during a computation and not in which state they terminate, indeed they may not be intended to terminate at all. For this reason they are often referred to as reactive systems, to distinguish them from traditional calculational systems, as e.g. a program calculating your income tax, for which the interesting behaviour is the answer it gives when (or if) it terminates, in other words the (possibly partial) function it computes between input and output. Church's thesis tells us that regardless of whether we choose the lambda calculus, Turing machines, or almost any modern programming language such as C or Java to describe calculational systems, we are able to describe exactly the same class of functions. However, there is no agreement on observable behaviour for concurrent reactive systems, and consequently there is no correspondent to Church's thesis. A result of this fact is that an overwhelming number of different and often competing notions of observable behaviours, primitive operations, languages and mathematical models for describing their semantics, have been proposed in the litterature on concurrency. The work
Event Structures as Presheaves  Two Representation Theorems
 In Proc. CONCUR'99, LNCS
, 1999
"... The category of event structures is known to embed fully and faithfully in the category of presheaves over pomsets. Here a characterisation of the presheaves represented by event structures is presented. The proof goes via a characterisation of the presheaves represented by event structures when the ..."
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Cited by 4 (2 self)
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The category of event structures is known to embed fully and faithfully in the category of presheaves over pomsets. Here a characterisation of the presheaves represented by event structures is presented. The proof goes via a characterisation of the presheaves represented by event structures when the morphisms on event structures are "strict" in that they preserve the partial order of causal dependency. 1
Linearity and nonlinearity in distributed computation
"... The copying of processes is limited in the context of distributed computation, either as a fact of life, often because remote networks are simply too complicated to have control over, or deliberately, as in the design of security protocols. Roughly, linearity is about how to manage without a presume ..."
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Cited by 3 (2 self)
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The copying of processes is limited in the context of distributed computation, either as a fact of life, often because remote networks are simply too complicated to have control over, or deliberately, as in the design of security protocols. Roughly, linearity is about how to manage without a presumed ability to copy. The meaning and mathematical consequences of linearity are studied for pathbased models of processes which are also models of affinelinear logic. This connection yields an affinelinear language for processes in which processes are typed according to the kind of computation paths they can perform. One consequence is that the affinelinear language automatically respects openmap bisimulation. A range of process operations (from CCS, CCS with processpassing, mobile ambients, and dataflow) can be expressed within the affinelinear language showing the ubiquity of linearity. Of course, process code can be sent explicitly to be copied. Following the discipline of linear logic, suitable nonlinear maps are obtained as linear maps whose domain is under an exponential. Different ways to make assemblies of processes lead to different choices of exponential; the nonlinear maps of only some of which will respect bisimulation.
Categorical Models for Fairness and a Fully Abstract Presheaf Semantics of SCCS with Finite Delay
 CTCS’99, LNCS
, 1999
"... We present a presheaf model for the observation of infinite as well as finite computations. We apply it to give a denotational semantics of SCCS with finite delay, in which the meanings of recursion are given by final coalgebras and meanings of finite delay by initial algebras of the process equatio ..."
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Cited by 3 (0 self)
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We present a presheaf model for the observation of infinite as well as finite computations. We apply it to give a denotational semantics of SCCS with finite delay, in which the meanings of recursion are given by final coalgebras and meanings of finite delay by initial algebras of the process equations for delay. This can be viewed as a first step in representing fairness in presheaf semantics. We give a concrete representation of the presheaf model as a category of generalised synchronisation trees and show that it is coreflective in a category of generalised transition systems, which are a special case of the general transition systems of Hennessy and Stirling. The open map bisimulation is shown to coincide with extended bisimulation of Hennessy and Stirling, which is essentially fair CTL*bisimulation. Finally we formulate Milners operation semantics of SCCS with finite delay in terms of generalised transition systems and prove that the presheaf semantics is fully abstract with respect to extended bisimulation.
Talagrand's Inequality in Hereditary Settings
, 1998
"... We develop a nicely packaged form of Talagrand's inequality that can be applied to prove concentration of measure for functions de ned by hereditary properties. We illustrate the framework with several applications from combinatorics and algorithms. We also give an extension of the inequality v ..."
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Cited by 2 (0 self)
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We develop a nicely packaged form of Talagrand's inequality that can be applied to prove concentration of measure for functions de ned by hereditary properties. We illustrate the framework with several applications from combinatorics and algorithms. We also give an extension of the inequality valid in spaces satisfying a certain negative dependence property and give some applications.
A Representation Result for Free Cocompletions
, 1999
"... Given a class F of weights, one can consider the construction that takes a small category C to the free cocompletion of C under weighted colimits, for which the weight lies in F . Provided these free F cocompletions are small, this construction generates a 2monad on Cat, or more generally on VCa ..."
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Cited by 1 (0 self)
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Given a class F of weights, one can consider the construction that takes a small category C to the free cocompletion of C under weighted colimits, for which the weight lies in F . Provided these free F cocompletions are small, this construction generates a 2monad on Cat, or more generally on VCat for monoidal biclosed complete and cocomplete V. We develop the notion of a dense 2monad on VCat and characterise free F cocompletions by dense KZmonads on VCat. We prove various corollaries about the structure of such 2monads and their Kleisli 2categories, as needed for the use of open maps in giving an axiomatic study of bisimulation in concurrency. This requires the introduction of the concept of a pseudocommutativity for a strong 2monad on a symmetric monoidal 2category, and a characterisation of it in terms of structure on the Kleisli 2category. 1 Introduction Given a class of small categories S, one can consider the construction that takes a small category C to the free co...