ing from the technique of dual pairs in functional analysis (Kelley, Nanmioka et al. 1963, ch. 5), they defined the objects of their category to be the triples hA; B; A\Omega B OE !?i, where A and B are arbitrary objects of an autonomous category V, and ? is a fixed object, chosen to become dualizing. A morphism from hA; B; OEi to hC; D; fli was defined as a pair hu : A ! C; B / D : vi of V-arrows, making the square A\Omega D A\Omega B C\Omega D ? u\Omega D<Fnan><Fnan> fflffl A\Omega v<Fnan><Fnan> // OE<Fnan><Fnan> fflffl fl<Fnan><Fnan> (1) Cofree equivalences, dualities and -autonomous categories 3 commute. This is the setting in which the autonomous structure of a Chu category was originally discovered. The starting point of the present paper is the fact that the category described by Chu is isomorphic to the comma category V=? ? , induced by the homming functor ? ? : V op \Gamma! V : A 7\Gamma! A ? = A \Gammaffi? : (2) By definition, the objects of V=? ? (i.e. Id V =?...

. Shared memory systems provide a contract to the programmer in the form of a consistency condition. The conditions of atomic memory and sequential consistency provide the illusion of a single memory module, as in the uniprocessor case. Weaker conditions improve performance by sacrificing the simple programming model. Consistency conditions are formulated without reference to details of the hardware on which programs execute. We define the notion of a hardware model, a set of limitations on the communication network (e.g., message delay assumptions) and processing nodes (e.g., amount of available memory). We examine the effects of several models on a representative set of consistency conditions. In each model, we show how the conditions are related, and show that some are not appropriate for that model. Our study is carried out through relatively complete implementations, state machines which exactly capture the possible behaviors of all implementations in a given model. In addition t...

We match up types and processes by putting values in correspondence with events, coproduct with (noninteracting) parallel composition, and tensor product with orthocurrence. We then bring types and processes into closer correspondence by broadening and unifying the semantics of both using Chu spaces and their transformational logic. Beyond this point the connection appears to break down; we pose the question of whether the failures of the corrrespondence are intrinsic or cultural. 1 Introduction Types-as-processes modernizes data-as-programs. It is the Curry-Howard propositions-as-types correspondence with propositions replaced by processes. To the extent that types and processes are both part of the working programmer 's toolkit, even more than propositions, the types-as-processes correspondence is more central to the practice of programming than propositions-astypes. Moreover the connection works out very well mathematically, at least up to a point. The similarities and differences ...

In this paper the correspondence between safe Petri nets and event structures, due to Nielsen, Plotkin and Winskel, is extended to arbitrary nets without self-loops, under the collective token interpretation. To this end we propose a more general form of event structure, matching the expressive power of such nets. These new event structures and nets are connected by relating both notions with configuration structures, which can be regarded as representations of either event structures or nets that capture their behaviour in terms of action occurrences and the causal relationships between them, but abstract from any auxiliary structure. A configuration structure can also be considered logically, as a class of propositional models, or—equivalently— as a propositional theory in disjunctive normal from. Converting this theory to conjunctive normal form is the key

This report focuses on research into models and logics for concurrency and their application in specifying, verifying, and implementing concurrent systems. This general area has become known as concurrency theory , and its roots may be traced back to the 1960s [Dij68, Pet62]. Our aim is to survey the rich collection of mature theories and models for concurrency that exist; to review the powerful specification, design, and verification methods and tools that have been developed; and to highlight ongoing active areas of research and suggest fruitful directions for future investigation. By focusing on concurrency theory and its use in verification, we necessarily omit consideration of other concurrency-related topics such as concurrency control in database systems, concurrent program debugging, operating systems, distributed system architecture, and real-time systems. The interested reader is referred to other working group reports, which address many of these topics.

This report summarises the development of a portable, persistent and generic tool for modelling, exploring and analysing the behaviour of concurrent systems. The design is based on the general Action language theory for nondeterministic concurrent programming languages, and hence the tool is called the Action language workbench. It has been developed using an algebraic style and implemented in the algebraic programming system APS. The generic algebraic-based approach enables workbench to be applied to many languages by means of rapid prototyping and generation of action languages. A number of applications of the workbench to concurrent constraint and coordination languages, as well as its probabilistic extension are reported. Currently the functionality of the tool is restricted to simulation. Further development of both the underlying theory and the tool is planned regarding the description of distributed systems and the ehnancement of the kinds of analyses which can be performed. 1 I...

This essay offers an overview of basic aspects and central development in Concurrency Theory based on formal languages. In particular, it focuses on the theory of Process Calculi. 1

We show that Chu spaces, a new formalism used to describe parallelism and information flow, provide uniform explanations for different choices of fuzzy methodology, such as choices of fuzzy logical operations, of membership functions, of defuzzification, etc. 1 What Are Chu Spaces? 1.1 World According to Classical Physics It is well known that measurements can change the measured object: e.g., most methods of chemical analysis destroy a part of the analyzed substance; testing a car often means damaging it, etc. However, in classical (pre-quantum) physics it was assumed that in principle, we can make this adverse influence as small as possible. Therefore, ideally, each measurement can be described as a function r(x) from the set of all objects X to the set K of all measurement results. These measurements lead to a complete knowledge in the sense that an object x can be uniquely reconstructed from the results r(x) of all such measurements. 1.2 Non-Determinism in Modern Physics: En...

ComK may be defined as the (cartesian closed) category of comonoids in chuK , or equivalently as dictionaries D for which any crossword over D has its main diagonal in D. Com 2 resembles Top, ordinary topological spaces. Common to both are the Alexandro# posets and the Scott DCPOs, while the topological space R and the dual DCPO < 0} jointly witness the incomparability of Com 2 and Top. Such comonoids support a notion of bitopology admitting limits simultaneously for convergence and divergence. We raise the questions of whether a comonoid in chu 2 can be fully specified in terms of its specialization order and omitted cuts, and which cuts are optional. These questions have been actively pursued for four weeks as of this writing on the theory-edge mailing list in response to Puzzle 1.5 starting with http://groups.yahoo.com/group/theory-edge/messages/6957.

We characterize Set as the final half-pointed category, and the Chu categories as the quasifinal split-pointed categories.