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A Relational Model of NonDeterministic Dataflow
 In CONCUR'98, volume 1466 of LNCS
, 1998
"... . We recast dataflow in a modern categorical light using profunctors as a generalisation of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fits ..."
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Cited by 27 (13 self)
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. We recast dataflow in a modern categorical light using profunctors as a generalisation of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fits with the view of categories of models for concurrency and the general treatment of bisimulation they provide. In particular it fits with the recent categorical formulation of feedback using traced monoidal categories. The payoffs are: (1) explicit relations to existing models and semantics, especially the usual axioms of monotone IO automata are read off from the definition of profunctors, (2) a new definition of bisimulation for dataflow, the proof of the congruence of which benefits from the preservation properties associated with open maps and (3) a treatment of higherorder dataflow as a biproduct, essentially by following the geometry of interaction programme. 1 Introduction A fundament...
Reaction and Control I. Mixing Additive and Multiplicative Network Algebras
 Logic Journal of the IGPL
, 1996
"... . This paper is included in a series aiming to contribute to the algebraic theory of distributed computation. The key problem in understanding MultiAgent Systems is to find a theory which integrates the reactive part and the control part of such systems. To this end we use the calculus of flownomi ..."
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Cited by 9 (2 self)
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. This paper is included in a series aiming to contribute to the algebraic theory of distributed computation. The key problem in understanding MultiAgent Systems is to find a theory which integrates the reactive part and the control part of such systems. To this end we use the calculus of flownomials. It is a polynomiallike calculus for representing flowgraphs and their behaviours. An `additive' interpretation of the calculus was intensively developed to study control flowcharts and finite automata. For instance, regular algebra and iteration theories are included in a unified presentation. On the other hand, a `multiplicative' interpretation of the calculus of flownomials was developed to study dataflow networks. The claim of this series of papers is that the mixture of the additive and multiplicative network algebras will contribute to the understanding of distributed computation. The role of this first paper is to present a few motivating examples. To appear in Journal of IGPL....
The algebra of stream processing functions
, 1996
"... Dataflow networks are a model of concurrent computation. They consist of a collection of concurrent asynchronous processes which communicate by sending data over FIFO channels. In this paper we study the algebraic structure of the data ow networks and base their semantics on stream processing funct ..."
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Cited by 8 (1 self)
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Dataflow networks are a model of concurrent computation. They consist of a collection of concurrent asynchronous processes which communicate by sending data over FIFO channels. In this paper we study the algebraic structure of the data ow networks and base their semantics on stream processing functions. The algebraic theory is provided by the calculus of flownomials which gives a unified presentation of regular algebra and iteration theories. The kernel of the calculus is an equational axiomatization called Basic Network Algebra (BNA) for flowgraphs modulo graph isomorphism. We show that the algebra of stream processing functions called SPF (used for deterministic networks) and the algebra of sets of stream processing functions called PSPF (used for nondeterministic networks) are BNA algebras. As a byproduct this shows that both semantic models are compositional. We also identify the additional axioms satisfied by the branching components that correspond to constants in these two algebraic theories. For the deterministic case we study in addition the coarser equivalence relation on networks given by the inputoutput behaviour and provide a correct and complete axiomatization.
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
An Algebra of Dataflow Networks
 Fundamenta Informaticae
, 1995
"... . This paper describes an algebraic framework for the study of dataflow networks, which form a paradigm for concurrent computation in which a collection of concurrently and asynchronously executing processes communicate by sending messages between ports connected via FIFO message channels. A syntact ..."
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Cited by 4 (1 self)
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. This paper describes an algebraic framework for the study of dataflow networks, which form a paradigm for concurrent computation in which a collection of concurrently and asynchronously executing processes communicate by sending messages between ports connected via FIFO message channels. A syntactic dataflow calculus is defined, having two kinds of terms which represent networks and computations, respectively. By imposing suitable equivalences on networks and computations, we obtain the free dataflow algebra, in which the dataflow networks with m input ports and n output ports are regarded as the objects of a category S n m , and the computations of such networks are represented by the arrows. Functors defined on S n m label each computation by the input buffer consumed and the output buffer produced during that computation, so that each S n m is a span in Cat. It is shown that the free dataflow algebra construction underlies a monad in the category of collections S = fS n m : m...
Trace Semantics Is Fully Abstract
, 2009
"... The discussion in the computerscience literature of the relative merits of linear versus branchingtime frameworks goes back to the early 1980s. One of the beliefs dominating this discussion has been that the lineartime framework is not expressive enough semantically, making lineartime logics la ..."
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Cited by 1 (0 self)
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The discussion in the computerscience literature of the relative merits of linear versus branchingtime frameworks goes back to the early 1980s. One of the beliefs dominating this discussion has been that the lineartime framework is not expressive enough semantically, making lineartime logics lacking in expressiveness. In this work we examine the branchinglinear issue from the perspective of process equivalence, which is one of the most fundamental concepts in concurrency theory, as defining a notion of equivalence essentially amounts to defining semantics for processes. We accept three principles that have been recently proposed for concurrentprocess equivalence. The first principle takes contextual equivalence as the primary notion of equivalence. The second principle requires the description of a process to specify all relevant behavioral aspects of the process. The third principle requires observable process behavior to be reflected in its input/output behavior. It has been recently shown that under these principles trace semantics for nondeterministic transducers is fully abstract. Here we consider two extensions of the earlier model: probabilistic transducers and asynchronous transducers. We show that in both cases trace semantics is fully abstract.
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"... We use Tarski's relational calculus to construct a model of linear temporal logic. Both discrete and dense time are covered and we obtain denotational domains for a large variety of reactive systems. Keywords : Relational algebra, reactive systems, temporal algebra, temporal logic. 1 ..."
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We use Tarski's relational calculus to construct a model of linear temporal logic. Both discrete and dense time are covered and we obtain denotational domains for a large variety of reactive systems. Keywords : Relational algebra, reactive systems, temporal algebra, temporal logic. 1
Extensions of Independence Models
"... The purpose of this progress report is to give an account of the scientific work I have carried out during the Ph.D. part A programme at BRICS 1 , University of Aarhus. The through subject is independence models for concurrency, which are models for distributed reactive systems that besides repres ..."
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The purpose of this progress report is to give an account of the scientific work I have carried out during the Ph.D. part A programme at BRICS 1 , University of Aarhus. The through subject is independence models for concurrency, which are models for distributed reactive systems that besides representing possible temporal orderings are capable of representing the causal ordering of events in the system. A formal comparison using category theory jointly with Vladimiro Sassone, of two concrete independence models is presented, namely the models of transition systems with independence and labelled asynchronous transition systems. These are suitable for giving semantics to CCSlike languages. Then we study an open decidability problem for a particular independence bisimulation; hereditary history preserving bisimulation, categorically identified by a span of open maps, and in particular applicable to the models above. Finally, we consider how to broaden the scope of independence models, c...
Process Algebra with Feedback
"... We consider process graphs over a set of pins, i.e. with multiple entries and exits. On process graphs modulo bisimulation, we can define all standard process algebra operators plus the feedback operator from flowchart theory. We provide a complete axiomatisation for finite processes. Considering th ..."
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We consider process graphs over a set of pins, i.e. with multiple entries and exits. On process graphs modulo bisimulation, we can define all standard process algebra operators plus the feedback operator from flowchart theory. We provide a complete axiomatisation for finite processes. Considering the onepoint pin structure, we get back standard process algebra. 1980 Mathematics Subject Classification (1985 revision): 68Q55, 68Q10, 68Q45. 1987 CR Categories: F.1.2, D.3.1, F.3.1, D.1.3. Key words & Phrases: process algebra, feedback, pin. Note: The research of the first two authors was supported in part by ESPRIT basic research action 7166, CONCUR2. 1 Introduction Semantics of process theory is often given in terms of graphs. The process graphs considered usually have exactly one entry and exactly one exit. In [BeS94], this was adapted to allow for multiple entries and multiple exits. The resulting model was used to model key constructs of ACP and of the algebra of flownomials [St...
Dataflow language embedded in CML
, 1994
"... In this paper, we show how one can embed KahnMcQueen style dataflow in CML. This allows one to combine the dataflow paradigm, in particular the ability to have feedback loops, with the higherorder features that CML provides. The context for this research was the development of a language for digit ..."
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In this paper, we show how one can embed KahnMcQueen style dataflow in CML. This allows one to combine the dataflow paradigm, in particular the ability to have feedback loops, with the higherorder features that CML provides. The context for this research was the development of a language for digital signal processing applications. This application demands that we take finite buffer sizes seriously. We accordingly develop techniques for guaranteeing that only finite buffers are needed. From the point of view of ML programmers the main interest in the present work is to show how one can build a new concurrent abstraction on top of the CML primitives. In particular one needs a nonobvious notion of dataflow process in order to make feedback possible while still preserving the possibility of abstraction of dataflow processes. i Contents 1 Introduction 1 2 Language Definition 2 2.1 Tokens : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2.2 Processes...