# Prochain Exposé

jeudi 30 mars, 14h, Salle Aurigny (D165)

Jérémie Chalopin

A counterexample to Thiagarajan's conjecture on regular event structures

We provide a counterexample to a conjecture by Thiagarajan (1996 and 2002) that regular prime event structures correspond exactly to finite 1-safe Petri nets. The same counterexample is used to disprove a closely related conjecture by Badouel, Darondeau, and Raoult (1999) that domains of regular event structures with bounded #-cliques are recognizable by finite trace automata. 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. A necessary condition for both conjectures to be true is that domains of respective regular event structures admit a regular nice labeling (which corresponds to a special coloring of the hyperplanes of the associated CAT(0) cube complex). To disprove these conjectures, we describe a regular event domain (with bounded #-cliques) that does not admit a regular nice labeling. Our counterexample is derived from an example by Wise (1996 and 2007) of a nonpositively curved square complex X with six squares, whose edges are colored in five colors, and whose universal cover X˜ is a CAT(0) square complex containing a particular plane with an aperiodic tiling.

# Exposés des semaines suivantes

jeudi 13 avril, 14h, Salle Aurigny (D165)

Didier Lime

Synthèse pour la couverture dans les réseaux de Petri paramétrés

To Be announced

jeudi 27 avril, 14h

Josef Widder

To be announced

To Be announced