Event structure

From HandWiki
Revision as of 07:12, 27 June 2023 by WikiEd2 (talk | contribs) (linkage)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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]\displaystyle{ (E,\leq,\#) }[/math] consists of

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

such that

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

See also

References