In this report, we present a new framework for the definition of various data-structures (including trees and arrays) together with a generic language of filters enabling a rule-based programming style of functions. This framework is implemented in an experimental language called MGS. The underlying notions funding our framework have a topological nature and make possible to extend the case-based definition of functions found in modern functional languages beyond algebraic data-structures. Keywords group-based data fields, group indexed data structure, path pattern, combinatorial matching, array pattern matching, Cayley graphs, rule based array transformation. The authors of this research report can be contacted at: La.M.I., CNRS UMR 8042 GENOPOLE – Université d ’ Évry Val d’Essonne

During a discussion taking place at WMC'01, G. Paun put the question of what could be computed only by moving symbols between membranes. In this paper we provide some elements of the answer, in a setting similar to tissue P systems, where the set of membranes is organized into a finite graph or into a Cayley graph, and using a very simple propagation process characterizing accretive growth. Our main result is to characterize the final configuration as a least fixed point and to establish two series of approximations that converge to it. All the notions introduced (Cayley graph of membranes, accretive rule and iteration) have been implemented in the MGS programming language and the two approximation series can be e#ectively computed in Pressburger arithmetics using the omega calculator in the case of Abelian Cayley graphs.