: 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 dataflow-like model of concurrent computation. The model consists of machines, which ...

. 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...

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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 dataflow-like 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...

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 fixed-point 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...

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.

A method for automated analysis of fault-tolerance of distributed systems is presented. It is based on a stream model of computation augmented with approximation constructs, and this facilitates efficient analysis. Analyses of a protocol for fault-tolerant moving agents and a reliable broadcast protocol illustrate the method.

This document proposes these theses: ffl First-class interpreters offer a flexible means of language extensibility. ffl A simple module system can provide: -- incremental specialization -- program construction rather than program organization -- static rather than dynamic composition of programs -- explicit rather than implicit control over composition The former two claims duplicate properties presently associated only with object-oriented programming, while we regard the latter two as improvements. 2 Introduction Software design is language design for particular problems. The functional programming community has stressed the power and flexibility of this view on many occasions [Hen82, AS85, Hug90, Wad87, HS88], and one of the goals of this thesis is to emphasize it once more. According to this point of view, a programming language is a vehicle for constructing problem-specific languages. Existing languages support this view to varying degrees, but few allow significant sem...