The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the semantics of nondeterministic dataflow. Profunctors are shown to play a key role in relating models for concurrency and to support an interpretation as higher-order processes (where input and output may be processes). Two recent directions of research are described. One is concerned with a language and computational interpretation for profunctors. This addresses the duality between input and output in profunctors. The other is to investigate general spans of event structures (the spans can be viewed as special profunctors) to give causal semantics to higher-order processes. For this it is useful to generalise event structures to allow events which “persist.”

: The paper shows that characterizing the causal relationship between significant events is an important but non-trivial aspect for understanding the behavior of distributed programs. An introduction to the notion of causality and its relation to logical time is given; some fundamental results concerning the characterization of causality are presented. Recent work on the detection of causal relationships in distributed computations is surveyed. The issue of observing distributed computations in a causally consistent way and the basic problems of detecting global predicates are discussed. To illustrate the major difficulties, some typical monitoring and debugging approaches are assessed, and it is demonstrated how their feasibility is severely limited by the fundamental problem to master the complexity of causal relationships. Keywords: Distributed Computation, Causality, Distributed System, Causal Ordering, Logical Time, Vector Time, Global Predicate Detection, Distributed Debugging, ...

In this paper we present a synthesis method that utilizes timing constraints to generate timed asynchronous circuits. By unfolding the cyclic graph specification of an asynchronous circuit into an infinite acyclic graph, we are able to use efficient algorithms to analyze the given timing constraints. We derive a sufficient condition for the removal of redundancy in the specification. Based on this condition, we only need to analyze a finite subgraph of the infinite acyclic graph for derivation of a correct implementation. To the reduced specification, we apply a systematic synthesis procedure that further optimizes the implementation based on the timing constraints. Using realistic circuit examples, we demonstrate that the resulting timed implementation can be significantly reduced in complexity from its speed-independent counterpart while remaining hazard-free under the given timing constraints.

. While types for name passing calculi have been studied extensively in the context of sorting of polyadic ß-calculus [5, 34, 9, 28, 32, 19, 33, 10, 17], the same type abstraction is not possible in the monadic setting, which was left as an open issue by Milner [21]. We solve this problem with an extension of sorting which captures dynamic aspects of process behaviour in a simple way. Equationally this results in the full abstraction of the standard encoding of polyadic ß-calculus into the monadic one: the sorted polyadic ß-terms are equated by a basic behavioural equality in the polyadic calculus if and only if their encodings are equated in a basic behavioural equality in the typed monadic calculus. This is the first result of this kind we know of in the context of the encoding of polyadic name passing, which is a typical example of translation of high-level communication structures into ß- calculus. The construction is general enough to be extendable to encodings of calculi with mo...

The events of a security protocol and their causal dependency can play an important role in the analysis of security properties. This insight underlies both strand spaces and the inductive method. But neither of these approaches builds up the events of a protocol in a compositional way, so that there is an informal spring from the protocol to its model. By broadening the models to certain kinds of Petri nets, a restricted form of contextual nets, a compositional eventbased semantics is given to an economical, but expressive, language for describing security protocols; so the events and dependency of a wide range of protocols are determined once and for all. The net semantics is formally related to a transition semantics, strand spaces and inductive rules, as well as trace languages and event structures, so unifying a range of approaches, as well as providing conditions under which particular, more limited, models are adequate for the analysis of protocols. The net semantics allows the derivation of general properties and proof principles which are demonstrated in establishing an authentication property, following a diagrammatic style of proof.

A temporal logic for causality (Tlc) is introduced. The logic is interpreted over causal structures corresponding to partial order executions of programs. For causal structures describing the behavior of a finite fixed set of processes, a Tlc-formula can, equivalently, be interpreted over their linearizations. The main result of the paper is a tableau construction that gives a singly-exponential translation from a Tlc formula ' to a Streett automaton that accepts the set of linearizations satisfying '. This allows both checking the validity of Tlc formulas and model-checking of program properties. As the logic Tlc does not distinguish among different linearizations of the same partial order execution, partial order reduction techniques can be applied to alleviate the state-space explosion problem of model-checking. 1 Introduction One of the most successful techniques for automatic verification of finite-state systems has been model-checking . A model-checking algorithm decides wheth...

In recent years, there has been a resurgence of interest in the design of asynchronous circuits due to their ability to eliminate clock skew problems, achieve average case performance, adapt to processing and environmental variations, provide component modularity, and lower system power requirements. Traditional academic asynchronous designs methods use unbounded delay assumptions, resulting in circuits that are verifiable, but ignore timing for simplicity, leading to unnecessarily conservative designs. In industry, however, timing is critical to reduce both chip area and circuit delay. Due to a lack of formal methods that handle timing information correctly, circuits with timing constraints usually require extensive simulation to gain confidence in the design. This thesis bridges this gap by introducing timed circuits in which explicit timing information is incorporated into the specification and utilized throughout the design procedure to optimize the implementation. Our timed circu...

Abstract. Modelling is becoming a necessity in studying biological signalling pathways, because the combinatorial complexity of such systems rapidly overwhelms intuitive and qualitative forms of reasoning. Yet, this same combinatorial explosion makes the traditional modelling paradigm based on systems of differential equations impractical. In contrast, agentbased or concurrent languages, such as κ [1–3] or the closely related BioNetGen language [4–10], describe biological interactions in terms of rules, thereby avoiding the combinatorial explosion besetting differential equations. Rules are expressed in an intuitive graphical form that transparently represents biological knowledge. In this way, rules become a natural unit of model building, modification, and discussion. We illustrate this with a sizeable example obtained from refactoring two models of EGF receptor signalling that are based on differential equations [11, 12]. An exciting aspect of the agent-based approach is that it naturally lends itself to the identification and analysis of the causal structures that deeply shape the dynamical, and perhaps even evolutionary, characteristics of complex distributed biological systems. In particular, one can adapt the notions of causality and conflict, familiar from concurrency theory, to κ, our representation language of choice. Using the EGF receptor model as an example, we show how causality enables the formalization of the colloquial concept of pathway and, perhaps more surprisingly, how conflict can be used to dissect the signalling dynamics to obtain a qualitative handle on the range of system behaviours. By taming the combinatorial explosion, and exposing the causal structures and key kinetic junctures in a model, agent- and rule-based representations hold promise for making modelling more powerful, more perspicuous, and of appeal to a wider audience. 1

: 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 ...

In this paper we formulate asynchronous diagnosis by means of hidden state history reconstruction, from alarm observations. We follow a so-called true concurrency approach, in which no global state and no global time is available. Instead, we use only local states in combination with a partial order model of time, in which local events are ordered if they are either generated on the same site, or related via some causality relation. Our basic mathematical tool is that of net unfoldings originating from the Petri net research area. This study was motivated by the problem of event correlation in telecommunications network management.