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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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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.
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.
Event structures with persistence
, 2008
"... Increasingly, the style of computation is changing. Instead of one machine running a program sequentially, we have systems with many individual agents running in parallel. The need for mathematical models of such computations is therefore ever greater. There are many models of concurrent computation ..."
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Cited by 1 (0 self)
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Increasingly, the style of computation is changing. Instead of one machine running a program sequentially, we have systems with many individual agents running in parallel. The need for mathematical models of such computations is therefore ever greater. There are many models of concurrent computations. Such models can, for example, provide a semantics to process calculi and thereby suggest behavioural equivalences between processes. They are also key to the development of automated tools for reasoning about concurrent systems. In this thesis we explore some applications and generalisations of one particular model – event structures. We describe a variety of kinds of morphism between event structures. Each kind expresses a different sort of behavioural relationship. We demonstrate the way in which event structures can model both processes and types of processes by recalling a semantics for Affine HOPLA, a higher order process language. This is given in terms of asymmetric spans of event structures. We show that such spans support a trace construction. This allows the modelling of feedback and suggests a semantics for nondeterministic dataflow processes in terms of spans. The semantics given is shown to be consistent with Kahn’s fixed point construction when we consider spans modelling deterministic processes. A generalisation of event structures to include persistent events is proposed. Based on previously described morphisms between classical event structures, we define several categories of event structures with persistence. We show that, unlike for the corresponding categories of classical event structures, all are isomorphic to Kleisli categories of monads
Categorical Structure of Asynchrony
"... There is no shortage of semantic models for networks of communicating processes. But it seems fair to say that there is a lack of unifying principles behind the multitude of models that have been suggested. The goal of the present paper is to use category theory to isolate some general, and hopefull ..."
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There is no shortage of semantic models for networks of communicating processes. But it seems fair to say that there is a lack of unifying principles behind the multitude of models that have been suggested. The goal of the present paper is to use category theory to isolate some general, and hopefully useful, properties of models of asynchronous communication. These properties might be taken as a basis for classifying and relating some of the existing models. The axioms that we suggest are neither claimed to be complete, nor
unknown title
, 2002
"... 1 Introduction Process calculi like CCS have been motivated and studied operationally, thus from the outset lacking the abstract mathematical treatment provided by a domain theory. Consequently, concurrency has become a rather separate study; in particular, higherorder and functional features as kno ..."
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1 Introduction Process calculi like CCS have been motivated and studied operationally, thus from the outset lacking the abstract mathematical treatment provided by a domain theory. Consequently, concurrency has become a rather separate study; in particular, higherorder and functional features as known from sequential programming are most often treated in an ad hoc fashion, if at all. The study of presheaf models of processes [1, 10] can be seen as an attempt to bring concurrency back within the realm of traditional denotational semantics by providing a domain theory for concurrent computation. In particular, presheaf models come with a builtin notion of bisimulation, derived from open maps [11].
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"... Presheaf models and process calculi Process calculi like CCS have been motivated and studied mathematical treatment provided by a domain ..."
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Presheaf models and process calculi Process calculi like CCS have been motivated and studied mathematical treatment provided by a domain
This document in subdirectoryRS/02/48/ Linearity in Process Languages
, 909
"... Reproduction of all or part of this work 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 BRICS Report Series publications. Copies may be obtained by contacting: BRICS ..."
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Reproduction of all or part of this work 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 BRICS Report Series publications. Copies may be obtained by contacting: BRICS
Abstract Categorical Structure of Asynchrony
"... We investigate a categorical framework for the semantics of asynchronous communication in networks of parallel processes. Abstracting from a category of asynchronous labeled transition systems, we formulate the notion of a categorical model of asynchrony as a uniformly traced monoidal category with ..."
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We investigate a categorical framework for the semantics of asynchronous communication in networks of parallel processes. Abstracting from a category of asynchronous labeled transition systems, we formulate the notion of a categorical model of asynchrony as a uniformly traced monoidal category with diagonals, such that every morphism is total and the focus is equivalent to a category of complete partial orders. We present a simple, nondeterministic, cpobased model that satisfies these requirements, and we discuss how to refine this model by an observational congruence. We also present a general construction of passing from deterministic to nondeterministic models, and more generally, from nonlinear to linear structure on a category.
Presheaf Models and Process Calculi
, 2002
"... Introduction Process calculi like CCS have been motivated and studied operationally, thus from the outset lacking the abstract mathematical treatment provided by a domain theory. Consequently, concurrency has become a rather separate study; in particular, higherorder and functional features as kno ..."
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Introduction Process calculi like CCS have been motivated and studied operationally, thus from the outset lacking the abstract mathematical treatment provided by a domain theory. Consequently, concurrency has become a rather separate study; in particular, higherorder and functional features as known from sequential programming are most often treated in an ad hoc fashion, if at all. The study of presheaf models of processes [3, 14] can be seen as an attempt to bring concurrency back within the realm of traditional denotational semantics by providing a domain theory for concurrent computation. Much of the work so far [4, 6, 7, 8, 9, 10, 27] has concentrated on developing the domain theory itself and on showing how to handle existing models and notions from process calculi within it. Meanwhile, a full operational understanding of presheaf models has still not been obtained. A sensible way to proceed would be to exploit the domain theory to define mathematically natural process calcu