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Weak Bisimulation and Open Maps (Extended Abstract)
, 1999
"... A systematic treatment of weak bisimulation and observational congruence on presheaf models is presented. The theory is developed with respect to a "hiding" functor from a category of paths to observable paths. Via a view of processes as bundles , we are able to account for weak morphisms (rough ..."
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A systematic treatment of weak bisimulation and observational congruence on presheaf models is presented. The theory is developed with respect to a "hiding" functor from a category of paths to observable paths. Via a view of processes as bundles , we are able to account for weak morphisms (roughly only required to preserve observable paths) and to derive a saturation monad (on the category of presheaves over the category of paths). Weak morphisms may be encoded as strong ones via the Kleisli construction associated to the saturation monad. A general
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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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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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.
Hypergraph Optimization Problems: Why is the Objective Function Linear?
, 1996
"... Choosing an objective function for an optimization problem is a modeling issue and there is no apriori reason that the objective function must be linear. Still, it seems that linear 01 programming formulations are overwhelmingly used as models for optimization problems over discrete structures ..."
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Choosing an objective function for an optimization problem is a modeling issue and there is no apriori reason that the objective function must be linear. Still, it seems that linear 01 programming formulations are overwhelmingly used as models for optimization problems over discrete structures. We show that this is not an accident. Under some reasonable conditions (from the modeling point of view), the linear objective function is the only possible one.
Twisted Systems
, 1999
"... Let J be a shape in some category Shp for which there is a functor : Shp Cat. A categorical transition system (or system) is a pair (J; (J) C) consisting of a shape labelled by a functor in a category in C. Suitable choices for Shp include categories of partial orders, graphs, higherdimensional ..."
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Let J be a shape in some category Shp for which there is a functor : Shp Cat. A categorical transition system (or system) is a pair (J; (J) C) consisting of a shape labelled by a functor in a category in C. Suitable choices for Shp include categories of partial orders, graphs, higherdimensional automata and other structures with intrinsic notions of states and transitions. The construction yields a category CTS(Shp; C). Systems generalize conventional labelled transition systems over which they have some advantages. By abandoning graphs as shapes it becomes possible to model concurrent and asynchronous computation. By labelling in a category, rather than an alphabet or term algebra, the actions of an algorithm or process can have much richer structure. Actions can be functions, partial functions, machine instructions or even processes. Of particular importance are twisted systems. These have the form (J; ] (J) C) where g (\Gamma) : Cat Cat is the twisted arrow category constructi...
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...
This document in subdirectory RS/96/48 / Scalings in Linear Programming: Necessary and Sufficient Conditions for Invariance
"... is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS ..."
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is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS
This document in subdirectory RS/96/50 / Hypergraph Optimization Problems: Why is the Objective Function Linear?
"... is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS ..."
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is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS