. 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...

. This paper is included in a series aiming to contribute to the algebraic theory of distributed computation. The key problem in understanding Multi-Agent Systems is to find a theory which integrates the reactive part and the control part of such systems. To this end we use the calculus of flownomials. It is a polynomial-like calculus for representing flowgraphs and their behaviours. An `additive' interpretation of the calculus was intensively developed to study control flowcharts and finite automata. For instance, regular algebra and iteration theories are included in a unified presentation. On the other hand, a `multiplicative' interpretation of the calculus of flownomials was developed to study dataflow networks. The claim of this series of papers is that the mixture of the additive and multiplicative network algebras will contribute to the understanding of distributed computation. The role of this first paper is to present a few motivating examples. To appear in Journal of IGPL....

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 dataflow 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 a...

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 di#erent 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.

. This paper describes an algebraic framework for the study of dataflow networks, which form a paradigm for concurrent computation in which a collection of concurrently and asynchronously executing processes communicate by sending messages between ports connected via FIFO message channels. A syntactic dataflow calculus is defined, having two kinds of terms which represent networks and computations, respectively. By imposing suitable equivalences on networks and computations, we obtain the free dataflow algebra, in which the dataflow networks with m input ports and n output ports are regarded as the objects of a category S n m , and the computations of such networks are represented by the arrows. Functors defined on S n m label each computation by the input buffer consumed and the output buffer produced during that computation, so that each S n m is a span in Cat. It is shown that the free dataflow algebra construction underlies a monad in the category of collections S = fS n m : m...

The discussion in the computer-science literature of the relative merits of linear- versus branching-time frameworks goes back to the early 1980s. One of the beliefs dominating this discussion has been that the linear-time framework is not expressive enough semantically, making linear-time logics lacking in expressiveness. In this work we examine the branching-linear issue from the perspective of process equivalence, which is one of the most fundamental concepts in concurrency theory, as defining a notion of equivalence essentially amounts to defining semantics for processes. We accept three principles that have been recently proposed for concurrentprocess equivalence. The first principle takes contextual equivalence as the primary notion of equivalence. The second principle requires the description of a process to specify all relevant behavioral aspects of the process. The third principle requires observable process behavior to be reflected in its input/output behavior. It has been recently shown that under these principles trace semantics for nondeterministic transducers is fully abstract. Here we consider two extensions of the earlier model: probabilistic transducers and asynchronous transducers. We show that in both cases trace semantics is fully abstract.

The paper presents a simple format for typed logics with states by adding a function for register update to standard typed lambda calculus. It is shown that universal validity of equality for this extended language is decidable (extending a well-known result of Friedman for typed lambda calculus) . This system is next extended to a full fledged typed dynamic logic, and it is illustrated how the resulting format allows for very simple and intuitive representations of dynamic semantics for natural language and denotational semantics for imperative programming. The proposal is compared with some alternative approaches to formulating typed versions of dynamic logics. Keywords: type theory, compositionality, denotational semantics, dynamic semantics 1 Introduction A slight extension to the format of typed lambda calculus is enough to model states (assignments of values to storage cells) in a very natural way. Let a set R of registers or storage cells be given. If we assume that the values...

We consider process graphs over a set of pins, i.e. with multiple entries and exits. On process graphs modulo bisimulation, we can define all standard process algebra operators plus the feedback operator from flowchart theory. We provide a complete axiomatisation for finite processes. Considering the one-point pin structure, we get back standard process algebra. 1980 Mathematics Subject Classification (1985 revision): 68Q55, 68Q10, 68Q45. 1987 CR Categories: F.1.2, D.3.1, F.3.1, D.1.3. Key words & Phrases: process algebra, feedback, pin. Note: The research of the first two authors was supported in part by ESPRIT basic research action 7166, CONCUR2. 1 Introduction Semantics of process theory is often given in terms of graphs. The process graphs considered usually have exactly one entry and exactly one exit. In [BeS94], this was adapted to allow for multiple entries and multiple exits. The resulting model was used to model key constructs of ACP and of the algebra of flownomials [St...

In this paper, we show how one can embed Kahn-McQueen style dataflow in CML. This allows one to combine the dataflow paradigm, in particular the ability to have feedback loops, with the higher-order features that CML provides. The context for this research was the development of a language for digital signal processing applications. This application demands that we take finite buffer sizes seriously. We accordingly develop techniques for guaranteeing that only finite buffers are needed. From the point of view of ML programmers the main interest in the present work is to show how one can build a new concurrent abstraction on top of the CML primitives. In particular one needs a nonobvious notion of dataflow process in order to make feedback possible while still preserving the possibility of abstraction of dataflow processes. i Contents 1 Introduction 1 2 Language Definition 2 2.1 Tokens : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2.2 Processes...

We use Tarski's relational calculus to construct a model of linear temporal logic. Both discrete and dense time are covered and we obtain denotational domains for a large variety of reactive systems. Keywords : Relational algebra, reactive systems, temporal algebra, temporal logic. 1