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Extra info for Membrane Computing: 12th International Conference, CMC 2011, Fontainebleau, France, August 23-26, 2011, Revised Selected Papers
As in most of our recent papers [1, 10–16, 21, 25–27], our preferred membrane structure is a directed graph (digraph) or one of its subclasses, such as a directed acyclic graph (DAG) or, occasionally, a (rooted) tree, or a more complex structure, such as a hypergraph or a multigraph; (undirected) graph structures can be emulated by symmetric digraphs. e. messages can travel along both forward or reverse arcs’ directions. Each arc has two labels—one at its tail and another at its head: note that this is an extension of the usual graph convention, where an arc has just one label.
This approach is a practical necessity, because: 1. It enables reasonably fast parsing and processing of subcomponents (practically impossible with string symbols) and 2. It allows us to describe an algorithm with a fixed size elementary alphabet and a fixed sized rule set, independent of the number of cells in the system (sometimes impossible with only atomic symbols). e. we consider all possible Parallel and Distributed Algorithms in P Systems 41 combinations between (1) an instantiation mode in min, max and (2) a rewriting mode in min, max.
Nicolescu approach, by selecting the most adequate ingredients for our quest and propose several extensions, which seem to “naturally” ﬁt into the existing P systems framework and are useful or even required for modelling fundamental distributed and parallel algorithms. e. the problem should be given by the P system itself, more speciﬁcally, by its topology, and not as externally encoded data, which is then fed into a diﬀerent P system. • The problem must be a fundamental or very challenging distributed problem.