Expressivity in the κ Family

In this paper we study implementation of κ calculus into nanoκ calculus – called self-assembling of κ in nk. The former is a model for molecular biology that rewrites graphs of molecules in one step; the latter is a calculus similar to κ that only admits binary interactions. We give a solution of the self-assembling of κ in nanoκ that is divergent and we show the nonexistence of deterministic solutions retaining “reasonable” properties.