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Concurrent Transition Systems
 Theoretical Computer Science
, 1989
"... : Concurrent transition systems (CTS's), are ordinary nondeterministic transition systems that have been equipped with additional concurrency information, specified in terms of a binary residual operation on transitions. Each CTS C freely generates a complete CTS or computation category C , whose ..."
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Cited by 40 (5 self)
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: Concurrent transition systems (CTS's), are ordinary nondeterministic transition systems that have been equipped with additional concurrency information, specified in terms of a binary residual operation on transitions. Each CTS C freely generates a complete CTS or computation category C , whose arrows are equivalence classes of finite computation sequences, modulo a congruence induced by the concurrency information. The categorical composition on C induces a "prefix" partial order on its arrows, and the computations of C are conveniently defined to be the ideals of this partial order. The definition of computations as ideals has some pleasant properties, one of which is that the notion of a maximal ideal in certain circumstances can serve as a replacement for the more troublesome notion of a fair computation sequence. To illustrate the utility of CTS's, we use them to define and investigate a dataflowlike model of concurrent computation. The model consists of machines, which ...
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 28 (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...
Concurrent Transition System Semantics of Process Networks
 In Fourteenth ACM Symposium on Principles of Programming Languages
, 1987
"... Using concurrent transition systems [Sta86], we establish connections between three models of concurrent process networks, Kahn functions, input /output automata, and labeled processes. For each model, we define three kinds of algebraic operations on processes: the product operation, abstractio ..."
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Cited by 9 (7 self)
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Using concurrent transition systems [Sta86], we establish connections between three models of concurrent process networks, Kahn functions, input /output automata, and labeled processes. For each model, we define three kinds of algebraic operations on processes: the product operation, abstraction operations, and connection operations. We obtain homomorphic mappings, from input/output automata to labeled processes, and from a subalgebra (called "input/output processes") of labeled processes to Kahn functions. The proof that the latter mapping preserves connection operations amounts to a new proof of the "Kahn Principle." Our approach yields: (1) extremely simple definitions of the process operations; (2) a simple and natural proof of the Kahn Principle that does not require the use of "strategies" or "scheduling arguments"; (3) a semantic characterization of a large class of labeled processes for which the Kahn Principle is valid, (4) a convenient operational semantics...
A Simple Generalization of Kahn's Principle to Indeterminate Dataflow Networks
 Semantics for Concurrency, Leicester
, 1990
"... Kahn's principle states that if each process in a dataflow network computes a continuous input/output function, then so does the entire network. Moreover, in that case the function computed by the network is the least fixed point of a continuous functional determined by the structure of the network ..."
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Cited by 8 (2 self)
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Kahn's principle states that if each process in a dataflow network computes a continuous input/output function, then so does the entire network. Moreover, in that case the function computed by the network is the least fixed point of a continuous functional determined by the structure of the network and the functions computed by the individual processes. Previous attempts to generalize this principle in a straightforward way to "indeterminate" networks, in which processes need not compute functions, have been either too complex or have failed to give results consistent with operational semantics. In this paper, we give a simple, direct generalization of Kahn's fixedpoint principle to a large class of indeterminate dataflow networks, and we prove that results obtained by the generalized principle are in agreement with a natural operational semantics. 1 Introduction Dataflow networks are a parallel programming paradigm in which a collection of concurrently and asynchronously executing s...
The Algebra of Stream Processing Functions
 THEORETICAL COMPUTER SCIENCE
, 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 dataflow 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 dataflow 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 a...
The expressive power of parallelism
, 1990
"... We explore an algebraic language for networks consisting of a fixed number of reactive units, communicating synchronously over a fixed linking structure. The language has only two operators: disjoint parallelism, where two networks are composed in parallel without any interconnections, and linking, ..."
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Cited by 6 (3 self)
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We explore an algebraic language for networks consisting of a fixed number of reactive units, communicating synchronously over a fixed linking structure. The language has only two operators: disjoint parallelism, where two networks are composed in parallel without any interconnections, and linking, where an interconnection is formed between two ports. The intention is that these operators correspond to the primitive steps when constructing networks, and that they therefore are conceptually simpler than the operators in existing process algebras. We investigate the expressive power of our language. The results are: (1) Definability of behaviours: with only three simple processing units, every finitestate behaviour can be constructed. (2) Definability of operators: we characterise the network operators which are definable within the language," these turn out to include most operators previously suggested for describing parallelism. Our results hold for any congruence between trace equivalence and observation equivalence.
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
Towards a Complete Hierarchy of Compositional Dataflow Models
 IN: PROC. THEORETICAL ASPECTS OF COMPUTER SOFTWARE, LNCS 526
, 1991
"... A dataflow network consists of nodes that communicate by passing data over unbounded FIFO channels. For dataflow networks containing only deterministic nodes, Kahn has presented a simple and elegant semantic model. However, the generalization of this model is not compositional for nondeterministi ..."
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Cited by 5 (0 self)
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A dataflow network consists of nodes that communicate by passing data over unbounded FIFO channels. For dataflow networks containing only deterministic nodes, Kahn has presented a simple and elegant semantic model. However, the generalization of this model is not compositional for nondeterministic networks. Past work has
Structural and Behavioural Equivalences of Networks
 Information and Computation
, 1991
"... We define an algebraic language for networks of synchronously communicating asynchronous processes. A node in the network may have several ports; a port is either external to the whole network or connected through a link to another port. The language contains two types of operations: parallel com ..."
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Cited by 4 (1 self)
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We define an algebraic language for networks of synchronously communicating asynchronous processes. A node in the network may have several ports; a port is either external to the whole network or connected through a link to another port. The language contains two types of operations: parallel composition of two networks, and interlinking of two external ports within a network. We interpret this language in two ways: first we give a structural semantics, where terms are mapped to graphs representing the structure of networks, and second we give a behavioural semantics, where terms are mapped to behaviour schemas. A schema corresponds to a behaviour parameterised on the behaviours of the network nodes. These semantics give rise to structural and behavioural equivalences. We compare the equivalences and give sound and complete axiomatisations. 4 1 Introduction Consider a network consisting of several nodes executing in parallel and synchronising over the links in the network. ...
Kahn Principle for Linear Dynamic Networks
, 1994
"... We consider dynamic Kahnlike data flow networks, i.e. networks consisting of deterministic processes each of which is able to expand into a subnetwork. The Kahn principle states that such networks are deterministic, i.e. that for each network we have that each execution provided with the same in ..."
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We consider dynamic Kahnlike data flow networks, i.e. networks consisting of deterministic processes each of which is able to expand into a subnetwork. The Kahn principle states that such networks are deterministic, i.e. that for each network we have that each execution provided with the same input delivers the same output. Moreover, the principle states that the output streams of such networks can be obtained as the smallest fixed point of a suitable operator derived from the network specification. This paper is meant as a first step towards a proof of this principle. For a specific subclass of dynamic networks, linear arrays of processes, we define a transition system yielding an operational semantics which defines the meaning of a net as the set of all possible interleaved executions. We then prove that, although on the execution level there is much nondeterminism, this nondeterminism disappears when viewing the system as a transformation from an input stream to an outpu...