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Relations in Concurrency
"... 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 seman ..."
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Cited by 263 (33 self)
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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 higherorder 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 higherorder processes. For this it is useful to generalise event structures to allow events which “persist.”
Detecting Causal Relationships in Distributed Computations: In Search of the Holy Grail
 In search of the holy grail. Distributed Computing
, 1994
"... : The paper shows that characterizing the causal relationship between significant events is an important but nontrivial 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 conce ..."
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Cited by 203 (4 self)
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: The paper shows that characterizing the causal relationship between significant events is an important but nontrivial 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, ...
An Improvement of McMillan's Unfolding Algorithm
 Formal Methods in System Design
, 1996
"... McMillan has recently proposed a new technique to avoid the state explosion problem in the verification of systems modelled with finitestate Petri nets. The technique requires to construct a finite initial part of the unfolding of the net. McMillan's algorithm for this task may yield initial parts ..."
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Cited by 180 (9 self)
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McMillan has recently proposed a new technique to avoid the state explosion problem in the verification of systems modelled with finitestate Petri nets. The technique requires to construct a finite initial part of the unfolding of the net. McMillan's algorithm for this task may yield initial parts that are larger than necessary (exponentially larger in the worst case). We present a refinement of the algorithm which overcomes this problem. 1 Introduction In a seminal paper [10], McMillan has proposed a new technique to avoid the state explosion problem in the verification of systems modelled with finitestate Petri nets. The technique is based on the concept of net unfolding, a well known partial order semantics of Petri nets introduced in [12], and later described in more detail in [4] under the name of branching processes. The unfolding of a net is another net, usually infinite but with a simpler structure. McMillan proposes an algorithm for the construction of a finite initial part...
Modeling Concurrency with Geometry
, 1991
"... The phenomena of branching time and true or noninterleaving concurrency find their respective homes in automata and schedules. But these two models of computation are formally equivalent via Birkhoff duality, an equivalence we expound on here in tutorial detail. So why should these phenomena prefer ..."
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Cited by 125 (13 self)
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The phenomena of branching time and true or noninterleaving concurrency find their respective homes in automata and schedules. But these two models of computation are formally equivalent via Birkhoff duality, an equivalence we expound on here in tutorial detail. So why should these phenomena prefer one home over the other? We identify dimension as the culprit: 1dimensional automata are skeletons permitting only interleaving concurrency, whereas true nfold concurrency resides in transitions of dimension n. The truly concurrent automaton dual to a schedule is not a skeletal distributive lattice but a solid one. We introduce true nondeterminism and define it as monoidal homotopy; from this perspective nondeterminism in ordinary automata arises from forking and joining creating nontrivial homotopy. The automaton dual to a poset schedule is simply connected whereas that dual to an event structure schedule need not be, according to monoidal homotopy though not to group homotopy. We conclude...
Event structure semantics for CCS and related languages
 Computer Science Department, Aarhus University
, 1982
"... rIJ ..."
Rulebased Modelling of Cellular Signalling
 Proceedings of the 18 th International Conference on Concurrency Theory (CONCUR’07), Lecture Notes in Computer Science
, 2007
"... 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 syste ..."
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Cited by 70 (18 self)
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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 agentbased 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 rulebased representations hold promise for making modelling more powerful, more perspicuous, and of appeal to a wider audience. 1
Diagnosis of Asynchronous Discrete Event Systems, a Net Unfolding Approach
 IEEE TRANS. ON AUTOMATIC CONTROL
, 2001
"... In this paper we formulate asynchronous diagnosis by means of hidden state history reconstruction, from alarm observations. We follow a socalled 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 ..."
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Cited by 65 (27 self)
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In this paper we formulate asynchronous diagnosis by means of hidden state history reconstruction, from alarm observations. We follow a socalled 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.
A Technique of State Space Search Based on Unfolding
 Formal Methods in System Design
, 1992
"... Unfoldings of Petri nets provide a method of searching the state space of concurrent systems without considering all possible interleavings of concurrent events. A procedure is given for constructing the unfolding of a Petri net, terminating the construction when it is sufficient to represent all re ..."
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Cited by 64 (0 self)
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Unfoldings of Petri nets provide a method of searching the state space of concurrent systems without considering all possible interleavings of concurrent events. A procedure is given for constructing the unfolding of a Petri net, terminating the construction when it is sufficient to represent all reachable markings. This procedure is applied to hazard and deadlock detection in asynchronous circuits. Examples are given of scalable systems with exponential size state spaces, but polynomial size unfoldings, including a distributed mutual exclusion ring circuit.
Concurrent Transition Systems
 Theoretical Computer Science
, 1989
"... : 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 ..."
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Cited by 40 (5 self)
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: 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 dataflowlike model of concurrent computation. The model consists of machines, which ...