models differ slightly in what clock values newly created tokens can have, i.e., whether newly created tokens can inherit the clock value of some input token of the transition, or whether newly created tokens always have clock value zero. We consider the former, more general, case.

Decision problems associated with the reachability analysis of (extended) Petri nets include *Reachability* (can a given marking reach another given marking?) and *Coverability* (can a given marking ultimately enable a given transition?).

While Reachability is undecidable for all these TPN models [@RVCE1999], Coverability is decidable using the well-quasi ordering approach of [@ACJT2000; @FS2001] and complete for the hyper-Ackermannian complexity class $F_{\omega^{\omega^\omega}}$ [@HSS2012]. With respect to Coverability, TPN are equivalent [@BFHR2010] to (linearly ordered) data nets [@LNORW2008].

The *Existential Coverability* problem for TPN asks, for a given place $p$ and transition $t$, whether there exists a number $m$ such that the marking $M(m) {{\overset{\text{\tinydef}}{=}}}m\cdot\{(p,{\boldsymbol{0}})\}$ ultimately enables $t$. Here, $M(m)$ contains exactly $m$ tokens on place $p$ with all clocks set to zero and *no other tokens*. This problem corresponds to checking safety properties in distributed networks of arbitrarily many (namely $m$) initially identical timed processes that communicate by handshake. A negative answer certifies that the 