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Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 457 (20 self)
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Least fixpoints as meanings of recursive definitions.
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...
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
Causality and True Concurrency: A Dataflow Analysis of the PiCalculus (Extended Abstract)
 PROCEEDINGS OF THE FOURTH INTERNATIONAL CONFERENCE ON ALGEBRAIC METHODOLOGY AND SOFTWARE TECHNOLOGY, JULY 1995 LECTURE NOTES IN COMPUTER SCIENCE, VOLUME 936
, 1995
"... ..."
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 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...
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
A Kahn principle for networks of nonmonotonic realtime processes
, 1992
"... We show that the inputoutput function computed by a network of asynchronous realtime processes is denoted by the unique fixed point of a Scott continuous functional even though the network or its components may compute a discontinuous function. This extends a wellknown principle of Kahn [Kahn, 1 ..."
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Cited by 5 (1 self)
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We show that the inputoutput function computed by a network of asynchronous realtime processes is denoted by the unique fixed point of a Scott continuous functional even though the network or its components may compute a discontinuous function. This extends a wellknown principle of Kahn [Kahn, 1974] to an important class of parallel systems that has resisted the traditional fixed point approach. We present a fully abstract ordertheoretic denotational semantics for networks of asynchronous realtime processes. The timesensitive nature of the component processes allows them to compute functions which are not Scott continuous, nor even monotonic, on the domain of timed message streams ordered by the usual prefix relation. Because of the discontinuous behavior of the components, the characterization of networks with nonmonotonic processes as fixed points of continuous functionals (the standard approach of denotational semantics, applied to untimed networks of monotonic processes by K...
On the Kahn principle and fair networks
, 1998
"... The Kahn Principle [Kah77, KM77] states that each node in an asynchronous deterministic network computes a continuous function from input histories to output histories, and the behavior of the network can be characterized as a least fixed point. Fairness [Par79] plays a vital but implicit role: the ..."
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Cited by 4 (3 self)
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The Kahn Principle [Kah77, KM77] states that each node in an asynchronous deterministic network computes a continuous function from input histories to output histories, and the behavior of the network can be characterized as a least fixed point. Fairness [Par79] plays a vital but implicit role: the Kahn Principle is only sound when network execution is assumed to be (weakly) fair. Kahn’s model does not extend easily to nondeterministic networks, since the obvious generalization to continuous relations on histories is not compositional [BA81]. Previous attempts to model nondeterministic networks have sought to remain faithful to Kahn’s spirit by retaining some form of continuity assumption; these approaches typically apply only to a limited class of network and do not deal adequately with fairness. We argue that for nondeterministic networks the assumption of continuity is not operationally justifiable, whereas fairness is still vital. We provide a compositional model for fair nondeterministic networks, based on trace sets which can be regarded as history relations “extended in time ” to allow for the possibility of interference during execution. For a deterministic network one can extract the Kahnstyle history function from the network’s trace set, showing that our model is a natural generalization of Kahn’s. 1 1
Connectedness and Synchronization
 In Images of Programming. North Holland Publ. Co
, 1991
"... this paper we supplement the taxonomy list above with another kind of semantical domains, namely we consider connected relations. In the most general setting connected relations are parametrized by a given domain D which obeys some specific finiteness conditions; we say that D is an Fdomain [RT3]. ..."
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Cited by 3 (3 self)
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this paper we supplement the taxonomy list above with another kind of semantical domains, namely we consider connected relations. In the most general setting connected relations are parametrized by a given domain D which obeys some specific finiteness conditions; we say that D is an Fdomain [RT3]. In the particular case when D is the domain of natural numbers, connected relations appeared first in [Maz1] under the name of multitrees. For connected relations one can define a natural version of synchronization (strong conjunction).