Event structures, trace automata, and Petri nets are fundamental models in concurrency theory. There exist nice interpretations of these structures as combinatorial and geometric objects and both conjectures can be reformulated in this framework. Namely, from a graph theoretical point of view, the domains of prime event structures correspond exactly to median graphs; from a geometric point of view, these domains are in bijection with CAT(0) cube complexes.
Thiagarajan conjectured that regular event structures correspond exactly to event structures obtained as unfoldings of finite 1-safe Petri nets. Using the combinatorial and geometric interpretations of event structures, we provide a counterexample to this conjecture. Our counterexample is derived from an example by Wise of a particular CAT(0) cube complex.
On the positive side, we show that event structures obtained as
uOn the positive side, we show that event structures obtained as unfoldings of finite 1-safe Petri nets correspond to the finite special cube complexes introduced by Haglund and Wise in the context of geometric group theory.
