## doi:10.1093/comjnl/bxh000 Events, Causality and Symmetry

### BibTeX

@MISC{Winskel_doi:10.1093/comjnl/bxh000events,,

author = {Glynn Winskel},

title = {doi:10.1093/comjnl/bxh000 Events, Causality and Symmetry},

year = {}

}

### OpenURL

### Abstract

The article discusses causal models, such as Petri nets and event structures, how they have been rediscovered in a wide variety of recent applications, and why they are fundamental to computer science. A discussion of their present limitations leads to their extension with symmetry. The consequences, actual and potential, are discussed.

### Citations

192 | Full abstraction for pcf
- Abramsky, Jagadeesan, et al.
- 2000
(Show Context)
Citation Context ...ial role in establishing causal dependencies. Mathematics and logic: The research cannot be divorced from questions in mathematics and logic. Event structures represent types, underlie game semantics =-=[5, 47]-=- and begin to appear as denotations of proofs [3, 24]; the need for symmetry also appears here and in the earlier but related geometry of interaction of Girard [38]. It is not clear if the bipartite n... |

149 | A categorical semantics of quantum protocols
- Abramsky
- 2004
(Show Context)
Citation Context ...e event structures above, but where not all histories need appear; the hope is that quantum event structures and their constructions would furnish denotational semantics for quantum-process languages =-=[4, 82, 87]-=-. Continuous processes: A dream in the early development of event structures (see [94]) was to extend them to continuous processes so opening up their application to physical processes—Nachbin’s text ... |

106 |
Scenarios: A model of non-determinate computation,” in
- Brock, Ackerman
- 1981
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Citation Context ...on between them. A compelling example comes from the early work of Brock and Ackerman who were the first to emphasize the difficulties in giving a compositional semantics to nondeterministic dataflow =-=[11]-=-, though our example is based on simplifications in the later work of Rabinovich and Trakhtenbrot, and Russell [71]. Nondeterministic dataflow—Brock-Ackerman anomaly ✲ ✲ Ai C[Ai] = ✲☛ F ✏ ✡ ✑ There ar... |

90 |
Categories of Asynchronous Systems
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(Show Context)
Citation Context ...❩ ❣ ��✒ ❣ ✻ ❩ ❩ ❣ ��✒ ❣ ✻ ��✐ ���� ✄ �✐ ����� ✄✗ � �✒ ✘✿ ✘✘ ✘✘✘✘ ❩ ❩ ❣ ��✒ ✻ ❣ A Petri net and its unfolding relation on its actions (technically, so that it forms an asynchronous transition system =-=[6, 81]-=-), it determines a Petri net [93]. The relations between the different forms of causal models are well understood. Despite this and their often very successful, specialized applications, causal models... |

58 | Events in security protocols
- Crazzolara, Winskel
- 2001
(Show Context)
Citation Context ...often unexpected areas of application: • Security protocols: for example, strand spaces are a form of event structure which support reasoning about secrecy and authentication through causal relations =-=[86, 22, 17]-=-; • Systems biology: biologists rediscovered Petri nets in the analysis of chemical pathways (with conditions standing for molecular species and events for reactions). Ideas from Petri nets and event ... |

53 | Fault detection and diagnosis in distributed systems: an approach by partially stochastic Petri Nets. Journal of Discrete Event Dynamical Systems 8(2):203–231
- Aghasaryan, Fabre, et al.
- 1998
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Citation Context ...hers have used or rediscovered causal models in providing a compositional semantics—see [71] and its references; • Network diagnostics: in the monitoring and fault diagnosis of communication networks =-=[9]-=-; • Logic of programs: in concurrent separation logic where some artificialities in Brookes’ pioneering soundness proof are obviated through a Petri-net model [43]; • Partial order model checking: fol... |

49 | Relating strands and multiset rewriting for security protocol analysis - Cervesato, Durgin, et al. - 2000 |

45 |
Dl-Dom,øins as & Model of Polymorphism
- Gunter, \Minskel
(Show Context)
Citation Context ...ain (C(E), ⊆)—in fact, when E is countable, a dI-domain as discovered by Berry, and all such are so obtained. In this way event structures can represent a rich variety of types, even for polymorphism =-=[19, 99]-=-. 2.1.3. Anomalies in domain theory Nondeterminism: For traditional (‘topological’) domain theory the problem of adjoining nondeterminism was solved by Plotkin through the introduction of powerdomains... |

36 | Hereditary history preserving bisimulations or what is the power of the future perfect in program logics
- Bednarczyk
- 1991
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Citation Context ...tems the equivalence obtained is the usual strong bisimulation of Milner and Park [60], while for event structures it is also independently known, and called hereditary historypreserving bisimulation =-=[7]-=-. We now show how to extend a category of models to a category of models with symmetry. We won’t describe this in fullest generality, but for the case in which C is a category with pullbacks with dist... |

14 |
Modèles complètement adéquats et stable des λ-calculs typés, thèse de Doctorat d’état
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(Show Context)
Citation Context ...be made of its ‘units’ of information? There are essentially two answers in the literature, the ‘topological,’ the most wellknown from Scott’s work, and the ‘temporal,’ arising from the work of Berry =-=[10]-=-: • Topological: the basic units of information are propositions describing finite properties; more information corresponds to more propositions being true. Functions are ordered pointwise. Domains ar... |

14 |
open maps and bisimulation
- Cattani, Winskel, et al.
- 2005
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Citation Context ...ry and combinatorics also find a mathematical home [32]. In fact much of the work reported here started in the search for an operational reading of specific semantics using higher-dimensional algebra =-=[16, 70, 71]-=- and the realization that denotations (as presheaves and profunctors) could sometimes be represented by event structures [69, 78]. As should be clear from the existing application areas the work on ca... |

12 | Presheaf models for the pi-calculus
- Cattani, Stark, et al.
- 1997
(Show Context)
Citation Context ...th suitable choices of paths, presheaf categories subsume existing models such as event structures, while supporting a range of type constructions, also for higher-order processes and name generation =-=[101, 16, 69, 15]-=-. Presheaf categories and the relations between them, expressed as profunctors, connect with the rich world of higher-dimensional algebra. In particular, the little-explored representation of processe... |

7 | Unique factorisation lifting functors and categories of linearly-controlled processes
- Bunge, Fiore
(Show Context)
Citation Context ...of higher-dimensional algebra. In particular, the little-explored representation of processes as ‘bundles’ is crucial in the general treatment of weak bisimulation, and its extension to causal models =-=[12, 31]-=-. But the mathematical advantages come at a cost, that of finding an operational reading. 2.3. Relations rediscovered From a historical perspective it is remarkable that so many of the models of proce... |

4 | A cartesian closed category of event structures with quotients
- Abbes
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Citation Context ... component are rarely rigid. Varying maps: There are uses for several different forms of maps on event structures: rigid, total and partial maps, demand maps and a variant of demand maps due to Abbes =-=[2]-=-. Changing the category generally changes important categorical constructions. One would like to settle on some basic maps and then have a systematic way to vary the nature of maps within it. Unfoldin... |

4 |
Limit preservation from naturality
- Caccamo, Winskel
- 2005
(Show Context)
Citation Context ...cs goes both ways; sometimes the computerscience need for frequent efficient and safe calculation can lead to methods which streamline or remove the hand-waving from, the usual mathematical arguments =-=[13, 53]-=-. Today it is hard to pinpoint one specification logic for causal models, though there have been several The Computer Journal Vol. 00 No. 0, 200812 Glynn Winskel suggestions and considerable ingenuit... |

4 | clones and distributive laws
- Curien, “Operads
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Citation Context ...amming languages and processes [16]; The Computer Journal Vol. 00 No. 0, 2008�� �� 6 Glynn Winskel categories of models for concurrent computation [16]; as a starting point for the theory of operads =-=[23]-=-; . . . The ‘relations’ arising from computation can often be represented, in a more computationally informative way, in terms of event structures, with event structures playing both the role of input... |

3 |
Event Structure Semantics for the Internal pi-calculus. CONCUR
- Crafa, Varacca, et al.
- 2007
(Show Context)
Citation Context ... in extending work on an event-structure semantics of the pi-Calculus [61] to the whole language because of the absence of a key algebraic operation—a form of new-name abstraction on event structures =-=[21]-=- . The anomalies have a common solution: a formal treatment of symmetry in processes. Consider the first, that stable spans are insufficient. One wishes to free up the choice of maps for the input and... |

2 |
Event Domains, Stable Functions and Proof Nets
- Abramsky
(Show Context)
Citation Context ...as causal sets in theories of quantum gravity [84]; • Hardware: in the design and analysis of asynchronous circuits [54]; • Types and proof: as representations of propositions as types, and of proofs =-=[37, 3, 24]-=-; • Nondeterministic dataflow: where numerous researchers have used or rediscovered causal models in providing a compositional semantics—see [71] and its references; • Network diagnostics: in the moni... |

2 |
Counting Paths: Nondeterminism as Linear Algebra
- Benson
- 1984
(Show Context)
Citation Context ...ses the set of ways of computing. Early suggestions along these lines were made by Lehman with a definition of a categorical powerdomain [56], Benson in ‘counting paths’ of nondeterministic processes =-=[8]-=- and by Girard in his ‘quantitative’ domain theory [36]. Both Lehman and Girard’s work fit directly within the broader view of domains as presheaf categories [16]. Causal models have reappeared in pro... |

2 |
Regular and exact completions Pure and Applied Algebra 125
- Carboni, Vitale
- 1998
(Show Context)
Citation Context ...ymmetry. f Examples (1) If the subcategory P of C is a groupoid (i.e. all its maps are isomorphisms), then all maps of C are open and the construction of SC from C coincides with its exact completion =-=[14]-=-. (2) For the categories of event structures (with partial, total or rigid maps), a symmetry equivalence on an event structure E corresponds to an isomorphism family S of bijections θ : x ∼ =S y betwe... |

1 |
Category theory: a programming language oriented introduction. Forthcoming book based on lecture notes
- Curien
- 2008
(Show Context)
Citation Context ... models (though see [83]); the graphical tensor calculus is however predominant in recent axiomatizations for quantum computation [4]. Perhaps it is a matter of time, and awaiting the right textbooks =-=[20]-=-. There are some shining examples of uses of topology and geometry to reason about processes [42, 41, 28]. The influence between computer science and mathematics goes both ways; sometimes the computer... |