Event structure
# 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 $(E,\leq ,\#)$ consists of

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

such that

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