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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 58 (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 ...
Requirements on the Execution of Kahn Process Networks
 Proc. of the 12th European Symposium on Programming, ESOP 2003
, 2003
"... Kahn process networks (KPNs) are a programming paradigm suitable for streamingbased multimedia and signalprocessing applications. ..."
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Cited by 40 (3 self)
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Kahn process networks (KPNs) are a programming paradigm suitable for streamingbased multimedia and signalprocessing applications.
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 , ..."
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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 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...
Compositional Relational Semantics for Indeterminate Dataflow Networks
, 1989
"... Given suitable categories T; C and functor F : T ! C, if X; Y are objects of T, then we define an (X; Y )relation in C to be a triple (R; r; ¯ r), where R is an object of C and r : R ! FX and ¯ r : R ! FY are morphisms of C. We define an algebra of relations in C, including operations of "rel ..."
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Cited by 17 (6 self)
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Given suitable categories T; C and functor F : T ! C, if X; Y are objects of T, then we define an (X; Y )relation in C to be a triple (R; r; ¯ r), where R is an object of C and r : R ! FX and ¯ r : R ! FY are morphisms of C. We define an algebra of relations in C, including operations of "relabeling," "sequential composition," "parallel composition," and "feedback," which correspond intuitively to ways in which processes can be composed into networks. Each of these operations is defined in terms of composition and limits in C, and we observe that any operations defined in this way are preserved under the mapping from relations in C to relations in C 0 induced by a continuous functor G : C ! C 0 . To apply the theory, we define a category Auto of concurrent automata, and we give an operational semantics of dataflowlike networks of processes with indeterminate behaviors, in which a network is modeled as a relation in Auto. We then define a category EvDom of "event domains," a (non...
Reactive Process Networks
 IN ACM INTERNATIONAL CONFERENCE ON EMBEDDED SOFTWARE (EMSOFT
, 2004
"... Data flow process networks are a good model of computation for streaming multimedia applications incorporating audio, video and/or graphics streams. Process networks are concurrent processes communicating streams of data through FIFO channels. They can be executed e#ciently and determinately on mult ..."
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Cited by 15 (2 self)
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Data flow process networks are a good model of computation for streaming multimedia applications incorporating audio, video and/or graphics streams. Process networks are concurrent processes communicating streams of data through FIFO channels. They can be executed e#ciently and determinately on multiprocessor platforms. However, such stream processing applications are becoming more dynamic, often requiring runtime reconfigurations. Moreover, stream processing is not always an application on its own, but may be a component of a larger application. This application, e.g. a game application, may be control oriented and event driven; events may interact with the streaming component and (re)configure it. In order to capture the interaction between reactive and streaming components as well as reconfiguration in dynamic stream processing, we introduce in this paper a formal, operational and compositional semantics of socalled reactive process networks. This operational semantics can serve as the basis for programming models that allow the programming of streaming components interacting with reactive system components and their reconfigurations. It also supports the construction of analysis and synthesis tools for dynamic streaming multimedia applications. It allows the integration of reactive behaviour in process networks as general as Kahn process networks, but it is also suitable for more restricted and e#cient classes of process networks.
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.
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 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...
The Expressive Power of Indeterminate Primitives in Asynchronous Computation
 Proceedings of the Fifteenth Conference on Foundations of Software Technology and Theoretical Computer Science, Lecture Notes In Computer Science
, 1995
"... It has long been realized that the exigencies of systems programming require primitives that behave indeterminately. The bestknown dataflow primitive is the so called fair merge which abstracts aspects of fair resource allocation. It has been known for about two deacdes that fair primitives lead t ..."
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Cited by 6 (2 self)
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It has long been realized that the exigencies of systems programming require primitives that behave indeterminately. The bestknown dataflow primitive is the so called fair merge which abstracts aspects of fair resource allocation. It has been known for about two deacdes that fair primitives lead to unbounded indeterminacy. Around seven years ago E. W. Stark, Vasant Shanbhogue and I discovered that various variants of fair merge primitives, all manifesting unbounded indeterminacy, were provably different. These differences are based on simple monotonicity properties. In the present paper I review these results and discuss some related phenomena involving a fair stack. I then describe results about fair splitting. These results are based on topological properties rather than simple ordertheoretic properties. This gives some basic insight into what can and cannot be described by oracles and the relative power of various oracles. Finally I describe a result, implicitly due to Jim Russel...