On sets of numbers accepted by P/T systems composed by join

Recently, some studies linked the computational power of abstract computing systems based on multiset rewriting to models of Petri nets and the computation power of these nets to their topology. In turn, the computational power of these abstract computing devices can be understood by just looking at their topology, that is, information flow.Here we continue this line of research by introducing J languages and proving that they can be accepted by place/transition systems whose underlying net is composed only by join. Moreover, we study how J languages relate to other families of formal languages.