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 ${\displaystyle (E,\leq ,\#)}$  consists of

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

such that

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