Multiset-Based Self-Assembly of Graphs

Issue title: New Frontiers in Scientific Discovery – Commemorating the Life and Work of Zdzislaw Pawlak

Article type: Research Article

Authors: Bernardini, Francesco | Brijder, Robert | Rozenberg, Grzegorz | Zandron, Claudio

Affiliations: Leiden Institute of Advanced Computer Science, Leiden University, Leiden, The Netherlands. E-mails: bernardi@liacs.nl, rbrijder@liacs.nl, rozenber@liacs.nl | Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli studi di Milano-Bicocca, Milano, Italy. E-mail: zandron@disco.unimib.it

Abstract: We present a model for self-assembly of graphs based on multisets and the formalism of membrane systems. The model deals with aggregates of cells which are defined as undirected graphs where a multiset over a fixed alphabet is assigned to each vertex. The evolution of these aggregates is determined by an application of multiset-based aggregation rules to enlarge the current structure as well as an application of membrane-systems-based communication rules to enable cells to exchange objects alongside the edges of the graph. We compare the generative power of selfassembly membrane systems with and without communication rules, and we characterise properties of the sets of graphs generated by these systems. We also introduce two notions of stability for self-assembly processes that capture the idea of having produced a stable structure. Finally, we investigate self-assembly membrane systems where the alphabet is a singleton.

Keywords: Multisets, Membrane Systems, Self-Assembly, Graph Generation

Journal: Fundamenta Informaticae, vol. 75, no. 1-4, pp. 49-75, 2007