E.W. Stark. Concurrent transition system semantics of process networks. In Proc. of the 1987 SIGACT-SIGPLAN Symposium on Principles of Programming Languages, Munich, Germany, January 1987, pages 199--210. ACM Press, 1987.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of KPNs touches on the Kahn Principle, stating that the solution to the network equations formulated by Kahn [7] is the same as the behaviour of a model of (sequential) programs reading and writing tokens on channels. The Principle was introduced, but not proved, by Kahn in [7] It was proved [5, 13] for an operational model of transition systems. Scheduling process networks using static bounded channels is extensively addressed by Thomas Parks in [12] introducing an algorithm that uses bounded memory if possible. Based on this scheduling policy, a number of tools and libraries have been ....

....exist in realistic networks. Further, when multiple KPNs are controlled by a single run time scheduler, one entire process network may get stuck in a deadlock. A deadlock detection scheme has to detect local deadlocks. It is well known that the Kahn Principle hinges on fair scheduling of processes [3, 7, 13]. Fairness means that all processes that can make progress should make progress at some point. This is often a tacit but valid assumption if the underlying realisation is truly concurrent, or fairly scheduled. In the context however of bounded FIFO channels where processes appear to be inactive ....

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E.W. Stark. Concurrent transition system semantics of process networks. In Proc. of the 1987 SIGACT-SIGPLAN Symposium on Principles of Programming Languages, Munich, Germany, January 1987, pages 199--210. ACM Press, 1987.

....Since Kahn s principle is a direct application of ideas from denotational semantics, it has perhaps seemed natural that investigations of how to extend this principle to indeterminate networks should be performed in a similar abstract semantic context. In my own studies of these issues [7, 11, 12, 14], I have consciously avoided committing to a particular syntax until I was confident that the syntax would clarify the underlying mathematical structure, rather than obscuring it amid a mass of irrelevant detail. I now feel confident enough to propose a particular syntactic formulation. The ....

E. W. Stark. Concurrent transition system semantics of process networks. In Fourteenth ACM Symposium on Principles of Programming Languages, pages 199--210, January 1987.

....our formal results, we will use the notion of traces of networks. Recent work by Jonsson [14] and Russell [31] shows that traces constitute a good abstraction of the detailed operational aspects of network behavior. An automata theoretic formalism essentially due to Lynch and Tuttle [22] and Stark [34] is presented in appendix A. We show how one can pass from these automata to traces of the networks, and then reason with traces exclusively after developing the machinery to reason about process equivalence and implementability. We use a very weak notion of process equivalence. The significance ....

....to McGill University. A Operational Semantics of Dataflow Processes In this appendix we describe the operational semantics of dataflow networks in terms of automata equipped with a notion of concurrent transition. The development here is essentially due to Lynch and Tuttle [21, 22] and Stark [34, 35]. We have included it in order to make the paper reasonably self contained. The operational semantics describes the execution of a program in terms of a sequence of transitions between states. We do not wish to get tied down to any particular machine, so we wish to define an abstract machine ....

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E. W. Stark. Concurrent transition system semantics of process networks. In Proceedings Of The Fourteenth Annual ACM Symposium On Principles Of Programming Languages, pages 199--210, 1987.

....transitions cannot be disabled by the arrival of input, we obtain the class of monotone port automata. We shall see that monotone port automata are an extremely well behaved class of indeterminate processes. Essentially the same class of automata was defined in a somewhat more abstract setting in [27], but was not thoroughly investigated there. After defining the various kinds of automata, we show how to compose a collection of component automata into a network automaton, which represents a system of concurrently executing processes in which communication and synchronization takes place ....

....happens to one redex in a term while others are contracted. Our use is entirely analogous a residual operation lets us keep track of what happens to one transition while other transitions are executed concurrently. The use of residuals in reasoning about concurrent systems was demonstrated in [27]. Before proceeding with the presentation of our results, we comment on notation. In this paper, all sets whose cardinality is left unspecified are assumed to be at most countable. If V is a set, then V and V 1 denote, respectively, the of all finite sequences from V , and the set of all ....

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E. W. Stark. Concurrent transition system semantics of process networks. In Proceedings Of The Fourteenth Annual ACM Symposium On Principles Of Programming Languages, pages 199--210, 1987.

....M , one can define a computation sequence of M to be a sequence of the form q 0 oe 1 Gamma q 1 oe 2 Gamma . oe n Gamma q n ; This paper is a revised and expanded version of [35] which it supersedes. Some of the results presented here were reported, in an abbreviated form, in [36]. where each q k is in Q, each oe k is in Sigma [ ffflg, and (q k ; oe k 1 ; q k 1 ) 2 Delta for each k. The string oe 1 oe 2 . oe n is called the trace of the computation. Here we regard the set Sigma as embedded in the free monoid Sigma in the obvious way, and regard ffl as the ....

E. W. Stark. Concurrent transition system semantics of process networks. In Fourteenth ACM Symposium on Principles of Programming Languages, pages 199--210, January 1987.

....in part by NSF Grants CCR 8702247 and CCR 8902215. of such processes also computes a continuous function, which can be characterized as the least fixed point of a continuous functional associated with the network. This elegant idea has been called the Kahn principle, and it has been shown [9, 21, 36] to give results in agreement with a natural token pushing operational semantics. In practical programming applications of the dataflow idea, the restriction to functional processes is somewhat limiting, because there are useful programs one wants to write that do not describe processes with ....

E. W. Stark. Concurrent transition system semantics of process networks. In Fourteenth ACM Symposium on Principles of Programming Languages, pages 199--210, January 1987.

....set difference. Let al.ph denote the category of concurrent alphabets and their morphisms. Concurrent alphabets constitute the starting point for trace theory [1, 12] The above definition of morphism of concurrent alphabets was motivated by the author s study of concurrent transition systems [16, 17, 18]. The category Alph has a number of pleasant properties, although the author is not aware of it having been studied previously. Lemma 3.1 Suppose : E F is a morphism of concurrent alphabets. If U[V 2 Com(E) then (1) U [ V ) U) V ) and (2) U V ) U) V ) Proof (1) ....

E. W. Stark. Concurrent transition system semantics of process networks. In Fourteenth ACM Symposium on Principles of Programming Languages, pages 199--210, January 1987.

....little work on relating these more abstract formulations to a concrete operational semantics. At least in the case of dataflow networks, perhaps the reason has been the lack of a suitable operational framework in which to perform such an investigation. The results of this paper and others [12, 18, 16, 15, 9], strengthen the authors conviction that monotone input output automata provide such a framework. The key feature of these automata that permits the operational analysis of networks is the fact that concurrency information is explicitly represented, allowing us to construct a domain of ....

....a subset of X Theta Y , called the input output relation of A. If the input output relation happens to be the graph of a function f : X Y , then we call f the function computed by A. The following correspondence between determinate automata and continuous functions was shown in [15], and forms a prototype after which our new results are patterned. Theorem 1 Determinate automata compute functions. Moreover, a function f : X Y is the function computed by a determinate automaton iff f is a continuous function. Proof Immediate from Proposition 4.4 and Proposition 4.5 ....

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E. W. Stark. Concurrent transition system semantics of process networks. In Fourteenth ACM Symposium on Principles of Programming Languages, pages 199--210, January 1987.

....all values from one input channel only in case the sequence of values arriving on the other channel is finite. Infinity fair merge (imerge) guarantees to transmit all values from one input channel only in case the sequence of values arriving on the other channel is infinite. In previous papers [15, 21, 22], we identified the networks of monotone processes as an interesting and particularly well behaved subclass of the class of indeterminate dataflow networks. The main result of [15] was that, although such networks can be used to perform the unfair merging operations amerge and imerge, no such ....

....We conclude this section with some additional facts about the computations of monotone input output automata. We do not use these facts explicitly in this paper, but they are helpful in understanding the behavior of these automata. Proofs can be found (in a somewhat more abstract setting) in [21, 22]. Proposition 5 A monotone automaton A has the following properties: 1. For every state q and input trace x, there exists a unique computation x (q) with dom( x (q) q and tr( x ) x. Moreover, the map : X Comp q (A) that takes x 2 X to x 2 Comp q (A) is a primeinterval ....

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E. W. Stark. Concurrent transition system semantics of process networks. In Fourteenth ACM Symposium on Principles of Programming Languages, pages 199--210, January 1987.

....be interpreted as saying something indirectly about definability. Our results, concerning the relative power of merging primitives, are a byproduct of a more general study of networks of dataflow like processes with indeterminate behavior. Our main tool in this study is a formalism developed in [25]. We define three classes of automata, starting with a very general, abstract class, and becoming successively more specialized and concrete. The first class, called simply automata, is essentially the same as the labeled transition systems that have been used in the study of CCS and CSP (e.g. ....

....transitions cannot be disabled by the arrival of input, we obtain the class of monotone port automata. We shall see that monotone port automata are an extremely well behaved class of indeterminate processes. Essentially the same class of automata was defined in a somewhat more abstract setting in [25], but was not thoroughly investigated there. After defining the various kinds of automata, we show how to compose a collection of component automata into a network automaton, which represents a system of concurrently executing processes in which communication and synchronization takes place ....

[Article contains additional citation context not shown here]

E. W. Stark. Concurrent transition system semantics of process networks. In Fourteenth ACM Symposium on Principles of Programming Languages, pages 199--210, January 1987.

....the notions of behavioral equivalence that are appropriate in this context. For some time, we have been studying a particular automata theoretic model for dataflow networks, in an attempt to identify whatever useful algebraic structure might be present. Based on the progress we have made so far [8, 9, 10, 13], a general structure appears to be emerging. However, all is not yet completely clear, and it continues to be difficult to identify and separate the important structure from the incidental artifacts of the model. In a previous paper [9] we showed that a dataflow network with input ports X and ....

E. W. Stark. Concurrent transition system semantics of process networks. In Fourteenth ACM Symposium on Principles of Programming Languages, pages 199--210, January 1987.

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