Abstract In this paper, we present an encoding of the $$\lambda $$ λ -calculus in a multiset rewriting system and provide a few applications of the construction. For this purpose, we choose the calculus named String MultiSet Rewriting, which was introduced in Barbuti et al. (Electron Notes Theor Comput Sci 194:19–34, 2008) by Barbuti et al. With the help of our encoding, we give alternative proofs for the standardization and the finiteness of developments theorems in the $$\lambda $$ λ -calculus.

We study the reversibility of communicating reaction systems, variants of networks of reaction systems communicating by sending reaction products to specific target components. We first consider the possibility of “backtracking” their computations, then define distributed communicating reaction systems, an “unsynchronized” variant of the model in order to show how reversibility can be defined in a causally consistent manner.