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1-Safe Petri nets and special cube complexes: equivalence and applications. (arXiv:1810.03395v1 [cs.LO])
来源于:arXiv
Nielsen, Plotkin, and Winskel (1981) proved that every 1-safe Petri net $N$
unfolds into an event structure $\mathcal{E}_N$. By a result of Thiagarajan
(1996 and 2002), these unfoldings are exactly the trace regular event
structures. Thiagarajan (1996 and 2002) conjectured that regular event
structures correspond exactly to trace regular event structures. In a recent
paper (Chalopin and Chepoi, 2017, 2018), we disproved this conjecture, based on
the striking bijection between domains of event structures, median graphs, and
CAT(0) cube complexes. On the other hand, in Chalopin and Chepoi (2018) we
proved that Thiagarajan's conjecture is true for regular event structures whose
domains are principal filters of universal covers of (virtually) finite special
cube complexes.
In the current paper, we prove the converse: to any finite 1-safe Petri net
$N$ one can associate a finite special cube complex ${X}_N$ such that the
domain of the event structure $\mathcal{E}_N$ (obtained as the unfoldi 查看全文>>