Event structure

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 $(E,\le ,\mathrm{\#})$ consists of

• a set $E$ of events
• a partial order relation on $E$ called causal dependency,
• an irreflexive symmetric relation $\mathrm{\#}$ called incompatibility (or conflict)

such that

• finite causes: for every event $e\in E$, the set $[e]=\{f\in E\mid f\le e\}$ of predecessors of $e$ in $E$ is finite
• hereditary conflict: for every events $d,e,f\in E$, if $d\le e$ and $d\mathrm{\#}f$ then $e\mathrm{\#}f$.

See also

• Binary relation
• Mathematical structure

References

• Winskel, Glynn (1987). "Event Structures". Advances in Petri Nets (Springer). http://www.cl.cam.ac.uk/~gw104/EvStr.pdf. 
• event structure in nLab