Viennot's geometric construction

2013-08-10T22:07:42Z

129.10.71.225: /* The construction */

In mathematics and computer science, an '''event structure''' represents a set of events, some of which can only be performed after another (there is a ''dependency'' between the events) and some of which might not be performed together (there is a ''conflict'' between the events).

== Formal definition ==
An '''event structure''' <math>(E,\leq,\#)</math> consists of
* a set <math>E</math> of '''events'''
* a [[partial order]] relation on <math>E</math> called '''causal dependency''',
* an [[irreflexive]] [[symmetric]] relation <math>\#</math> called '''incompatibility''' (or '''conflict''')
such that
* ''finite causes'': for every event <math>e\in E</math>, the set <math>[e]=\{f\in E|f\leq e\}</math> of predecessors of <math>E</math> is finite
* ''hereditary conflict'': for every events <math>d,e,f\in E</math>, if <math>d\leq e</math> and <math>d\# f</math> then <math>e\# f</math>.

== References ==
* {{cite article | last = Winskel | first = Glynn | url = http://www.cl.cam.ac.uk/~gw104/EvStr.pdf | title = Event Structures | journal = Advances in Petri Nets | publisher = Springer | series = Lecture Notes in Computer Science | year = 1987}}

[[Category:Computing terminology]]

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Viennot's geometric construction