P Systems and Topology: Some Suggestions for Research

Lately, some studies linked the computational power of abstract computing systems based on multiset rewriting to 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 just looking at their topology, that is, information flow. This line of research is very promising for several aspects: its results are valid for a broad range of systems based on multiset rewriting; it allows to know the computational power of abstract computing devices without tedious proofs based on simulations; it links computational power to topology and, in this way, it opens a broad range of questions. In this note we summarize the known result on this topic and we list a few suggestions for research together with the relevance of possible outcomes.