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Discrete Mathematics and Theoretical Computer Science DMTCS vol. 8, 2006, 249272 A Cartesian Closed Category of Event

Summary: Discrete Mathematics and Theoretical Computer Science DMTCS vol. 8, 2006, 249­272
A Cartesian Closed Category of Event
Structures with Quotients
Samy Abbes
LIAFA ­ Universit´e Paris 7. France
received Feb 8, 2006, revised May 23, 2006, accepted Sep 3, 2006.
We introduce a new class of morphisms for event structures. The category obtained is cartesian closed, and a natural
notion of quotient event structure is defined within it. We study in particular the topological space of maximal con-
figurations of quotient event structures. We introduce the compression of event structures as an example of quotient:
the compression of an event structure E is a minimal event structure with the same space of maximal configurations
as E.
Keywords: event structure, maximal elements, quotient semantics
1 Introduction
Prime event structures--we say event structures for short, always meaning prime event structures--have
been introduced by Winskel as a model of concurrent computational processes [14]. Applications of event
structures to concurrency theory are numerous, in particular to the theory of Petri nets and to trace theory
[11, 13, 12]. An event structure is defined as a triple (E, , #), where (E, ) is a poset whose elements
are called events, and # is a binary symmetric and irreflexive relation satisfying e1#e2 e3 e1#e3.
The order relation is called the causality relation, while the relation # is called the conflict relation. An
event structure E--we identify event structures and sets of events--is called finitary if E is a countable


Source: Abbes, Samy - Laboratoire Preuves, Programmes et Systèmes, Université Paris 7 - Denis Diderot


Collections: Computer Technologies and Information Sciences