Numerical networks of cells

Abstract

Numerical P systems (NPS) are a very particular class of P systems having important differences from most models in this area. The main particularity of the model is the usage of numerical variables whose values are shared among applicable rules, contrary to the concurrence for objects in the multiset for the traditional P systems case. In 2007, Freund and Verlan developed a formal framework for P systems to capture most of the essential features of P systems and to define their functioning in a formal way. Subsequent papers developed versions of this framework for the case of spiking neural P systems and P systems with dynamically evolving structure. These results permitted to obtain a different view on P systems giving a general framework to analyze, relate and extend different variants of P systems and other related models, like Petri nets or register machines. This paper aims to provide a similar generalization for the case of numerical P systems (NPS) and related variants like enzymatic or generalized NPS. We call the obtained model Numerical Networks of Cells (NNC). As in the case of the formal framework it allows to accurately describe NPS, as well as other types of P systems like those using fuzzy sets as computation support. Also, the new model generalizes other well-known models like Boolean networks or reaction systems and this can potentially help to bring bridges between P systems and these areas.