. 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...

Introduction "Geometry and Concurrency" is not yet a well-established domain of research, but is rather made of a collection of seemingly related techniques, algorithms and formalizations, coming from different application areas, accumulated over a long period of time. There is currently a certain amount of effort made for unifying these (in particular see the article (Gunawardena, 1994)), following the workshop "New Connections between Computer Science and Mathematics" held at the Newton Institute in Cambridge, England in November 1995 (and sponsored by HP/BRIMS). More recently, the first workshop on the very same subject has been held in Aalborg, Denmark (see http://www.math.auc.dk/~raussen/admin/workshop/workshop.html where the articles of this issue, among others, have been first sketched. But what is "Geometry and Concurrency" composed of then? It is an area of research made of techniques which use geometrical reasoning for describing and solving problems

Dataflow models of computation have intrigued computer scientists since the 1970s. They were first introduced by Jack Dennis as a basis for parallel programming languages and architectures, and by Gilles Kahn as a model of concurrency. Interest in these models of computation has been recently rekindled by the resurrection of parallel computing, due to the emergence of multicore architectures. However, Dennis and Kahn approached dataflow very differently. Dennis ’ approach was based on an operational notion of atomic firings driven by certain firing rules. Kahn’s approach was based on a denotational notion of processes as continuous functions on infinite streams. This paper bridges the gap between these two points of view, showing that sequences of firings define a continuous Kahn process as the least fixed point of an appropriately constructed functional. The Dennis firing rules are sets of finite prefixes satisfying certain conditions that ensure determinacy. These conditions result in firing rules that are strictly more general than the blocking reads of the Kahn-MacQueen implementation of Kahn process networks, and solve some compositionality problems in the dataflow model. 1

This paper investigates probability in the presence of causal dependence. More precisely, it studies the process model of probabilistic event structures. In their simplest form probabilistic choice is localised to cells at which immediate conflict arises; in which case probabilistic independence coincides with causal independence. An event structure is associated with a domain—that of its configurations ordered by inclusion. In domain theory probabilistic processes are denoted by continuous valuations on a domain. A key result of this paper is a representation theorem showing how continuous valuations on the domain of a confusion free event structure correspond to the probabilistic event structures it supports. Via a notion of tests, probabilistic event structures are related to another approach to probabilistic processes, viz. Markov decision processes. Tests and morphisms of event structures point the way to a more general theory in which, for example, event structures need not be confusion free. 1

We compare synchronous dataflow (SDF) and cyclo-static dataflow (CSDF), which are each special cases of a model of computation we call dataflow process networks. In SDF, actors have static firing rules: they consume and produce a fixed number of data tokens in each firing. This model is well suited to multirate signal processing applications and lends itself to efficient, static scheduling, avoiding the runtime scheduling overhead incurred by general implementations of process networks. In CSDF, which is a generalization of SDF, actors have cyclicly changing firing rules. In some situations, the added generality of CSDF can unnecessarily complicate scheduling. We show how higher-order functions can be used to transform a CSDF graph into a SDF graph, simplifying the scheduling problem. In other situations, CSDF has a genuine advantage over SDF: simpler precedence constraints. We show how this makes it possible to eliminate unnecessary computations and expose additional parallelism. We use digital sample rate conversion as an example to illustrate these advantages of CSDF.

In this paper, an approach to symbolic model checking of process networks is introduced. It is based on interval decision diagrams (IDDs), a representation of multi-valued functions. Compared to other model checking strategies, IDDs show some important properties that enable the verification of process networks more adequately than with conventional approaches. Additionally, applications concerning scheduling will be shown. A new form of transition relation representation called interval mapping diagrams (IMDs)---and their less general version predicate action diagrams (PADs)---is explained together with the corresponding methods. 1 Introduction Process network models---consisting in general of concurrent processes communicating through unidirectional FIFO queues---as that of Kahn [7, 8] are commonly used, e.g., for specification and synthesis of distributed systems. They form the basis for applications such as real-time scheduling and allocation. Many other models of computation, ...

this paper, we discuss alternative approaches to the realization of this principle, which holds that properties of program components should be preserved when those components are composed in parallel with other program components. We review two programming languages, Strand and Program Composition Notation, that support compositionality via a small number of simple concepts, namely monotone operations on shared objects, a uniform addressing mechanism, and parallel composition. Both languages have been used extensively for large-scale application development, allowing us to provide an informed assessment of their strengths and weaknesses. We observe that while compositionality simplifies development of complex applications, the use of specialized languages hinders reuse of existing code and tools, and the specification of domain decomposition strategies. This suggests an alternative approach based on small extensions to existing sequential languages. We conclude the paper with a discussion of two languages that realize this strategy. Categories and Subject Descriptors: D.3.2 [Programming Languages]: Language Classifications ---Concurrent, distributed, and parallel languages; D.3.3 [Programming Languages]: Language Constructs and Features---Concurrent programming structures General Terms: Languages Additional Key Words and Phrases: Compositionality, Parallel Languages, Parallel Programming ACM Transactions on Programming Languages and Systems, Vol. 8, No. 1, January 1999. Compositional Parallel Programming Languages \Delta 113 1. INTRODUCTION Parallel programming is widely regarded as difficult: more difficult than sequential programming, and perhaps (at least this is our view) more difficult than it needs to be. In addition to the normal programming concerns, the para...

We investigate the power of Kahn-style dataflow networks, with processes that may exhibit indeterminate behavior. Our main result is a theorem about networks of "monotone" processes, which shows: (1) that the input/output relation of such a network is a total and monotone relation; and (2) every relation that is total, monotone, and continuous in a certain sense, is the input/output relation of such a network. Now, the class of monotone networks includes networks that compute arbitrary continuous input/output functions, an "angelic merge" network, and an "infinity-fair merge" network that exhibits countably indeterminate branching. Since the "fair merge" relation is neither monotone nor continuous, a corollary of our main result is the impossibility of implementing fair merge in terms of continuous functions, angelic merge, and infinity-fair merge. Our results are established by applying the powerful technique of "residuals" to the computations of a network. Residuals, which have previ...

A common metric of speed for DSP systems is their throughput. Algorithm transformations are the key to obtaining high throughput ASIC as well as software implementations. However, increasingly DSP subsystems are being used in systems such as "signal processing servers" and embedded controllers where both throughput and latency are important, and independent, metrics of speed. For example, the subsystem implementing the control law in a robot controller is part of a feedback loop so that not only does it have to process the inputs arriving at a rate determined by the sample period of the control loop, but it also has to produce the output corresponding to an input sample within a specified latency constraint. Although throughput alone can be arbitrarily improved for several classes of systems using previously published techniques, none of those approaches are effective when latency constraints are considered. After formally establishing the relationship between latency and throughput in...

Integrated provenance support promises to be a chief advantage of scientific workflow systems over script-based alternatives. While it is often recognized that information gathered during scientific workflow execution can be used automatically to increase fault tolerance (via checkpointing) and to optimize performance (by reusing intermediate data products in future runs), it is perhaps more significant that provenance information also may be used by scientists to reproduce results from earlier runs, to explain unexpected results, and to prepare results for publication. Current workflow systems offer little or no direct support for these “scientist-oriented ” queries of provenance information. Indeed the use of advanced execution models in scientific workflows (e.g., process networks, which exhibit pipeline parallelism over streaming data) and failure to record certain fundamental events such as state resets of processes, can render existing provenance schemas useless for scientific applications of provenance. We develop a simple provenance model that is capable of supporting a wide range of scientific use cases even for complex models of computation such as process networks. Our approach reduces these use cases to database queries over event logs, and is capable of reconstructing complete data and invocation dependency graphs for a workflow run.