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29
A Proof of the Kahn Principle for Input/Output Automata
 Information and Computation
, 1989
"... We use input/output automata to define a simple and general model of networks of concurrently executing, nondeterministic processes that communicate through unidirectional, named ports. A notion of the input/output relation computed by a process is defined, and determinate processes are defined to ..."
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Cited by 63 (8 self)
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We use input/output automata to define a simple and general model of networks of concurrently executing, nondeterministic processes that communicate through unidirectional, named ports. A notion of the input/output relation computed by a process is defined, and determinate processes are defined to be processes whose input/output relations are singlevalued. We show that determinate processes compute continuous functions, and that networks of determinate processes obey Kahn's fixedpoint principle. Although these results are already known, our contribution lies in the fact that the input/output automata model yields extremely simple proofs of them (the simplest we have seen), in spite of its generality. 1 Introduction Kahn (1974) describes a simple parallel programming language based on the concept of a network of concurrently executing sequential processes that can communicate by sending values over "channels. " The communication primitives available to processes are sufficiently ...
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...
An Algebraic View on the Semantics of Model Composition
 Model Driven Architecture  Foundations and Applications (ECMDAFA), volume 4530 of LNCS
, 2007
"... Abstract. Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide several complementary views on the system to be de ..."
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Cited by 21 (11 self)
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Abstract. Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide several complementary views on the system to be developed. This however leads to a need for compositional models. This paper describes a foundational theory of model composition in form of an algebra to explicitly clarify different variants and uses of composition, their interplay with the semantics of the involved models and their composition operators.
The expressive power of indeterminate dataflow primitives
 Information and Computation
, 1992
"... We analyze the relative expressive power of variants of the indeterminate fair merge operator in the context of static dataflow. We establish that there are three different, provably inequivalent, forms of unbounded indeterminacy. In particular, we show that the wellknown fair merge primitive canno ..."
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Cited by 17 (7 self)
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We analyze the relative expressive power of variants of the indeterminate fair merge operator in the context of static dataflow. We establish that there are three different, provably inequivalent, forms of unbounded indeterminacy. In particular, we show that the wellknown fair merge primitive cannot be expressed with just unbounded indeterminacy. Our proofs are based on a simple trace semantics and on identifying properties of the behaviors of networks that are invariant under network composition. The properties we consider in this paper are all generalizations of monotonicity. 1
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 14 (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.
Relational Semantics of NonDeterministic Dataflow
, 1997
"... We recast dataflow in a modern categorical light using profunctors as a generalization 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 fit ..."
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Cited by 12 (5 self)
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We recast dataflow in a modern categorical light using profunctors as a generalization 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.
Equational Reasoning About Nondeterministic Processes
 FORMAL ASPECTS OF COMPUTING
, 1990
"... A deterministic messagecommunicating process can be characterized by a "continuous" function f which describes the relationship between the inputs and the outputs of the process. The operational behavior of a network of deterministic processes can be deduced from the least fixpoint of a f ..."
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Cited by 11 (2 self)
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A deterministic messagecommunicating process can be characterized by a "continuous" function f which describes the relationship between the inputs and the outputs of the process. The operational behavior of a network of deterministic processes can be deduced from the least fixpoint of a function g, where g is obtained from the functions that characterize the component processes of the network. We show in this paper that a nondeterministic process can be characterized by a "description" consisting of a pair of functions. The behavior of a network consisting of such processes can be obtained from the "smooth" solutions of the descriptions characterizing its component processes. The notion of smooth solution is a generalization of least fixpoint. Descriptions enjoy the crucial property that a variable may be replaced by its definition.
A Domaintheoretic Model for a Higherorder Process Calculus
 Proceedings of the 17th International Colloquium on Automata Languages and Programming
, 1996
"... In this paper we study a higherorder process calculus, a restriction of one due to Boudol, and develop an abstract, model for it. By abstract we mean that the model is constructed domaintheoretically and reflects a certain conceptual viewpoint about observability. It is not constructed from the sy ..."
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Cited by 11 (2 self)
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In this paper we study a higherorder process calculus, a restriction of one due to Boudol, and develop an abstract, model for it. By abstract we mean that the model is constructed domaintheoretically and reflects a certain conceptual viewpoint about observability. It is not constructed from the syntax of the calculus or from computation sequences. We describe a new powerdomain construction that can be given additional algebraic structure that allows one to model concurrent composition, in the same sense that Plotkin's powerdomain can have a continuous binary operation defined on it to model choice. We show that the model constructed this way is adequate with respect to the operational semantics. The model that we develop and our analysis of it is closely related to the work of Abramsky and Ong on the lazy lambda calculus. 1 Introduction A fundamental problem in the semantics of parallel programming languages is integrating concurrency with abstraction. Kahn's pioneering work on stat...
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 net ..."
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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...
Arithmetic + Logic + Geometry = Concurrency
 In Proc. First Latin American Symposium on Theoretical Informatics, LNCS 583
, 1992
"... This paper ties together three primitivist views of concurrency whose development the author has had some involvement with, namely the arithmetic of schedules, the logic of scheduleautomaton duality, and the geometry of automata. Separately each of these views shed considerable light on concurrency ..."
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Cited by 7 (3 self)
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This paper ties together three primitivist views of concurrency whose development the author has had some involvement with, namely the arithmetic of schedules, the logic of scheduleautomaton duality, and the geometry of automata. Separately each of these views shed considerable light on concurrency. Our goal here is to bring these three views together coherently in the one place. The general picture is as follows. 1 2 3 Arithmetic of Schedules