Computing with Membranes: Variants with an Enhanced Membrane Handling

Abstract

Membrane computing is a recently introduced (very general) computing framework which abstracts from the way the living cells process chemical compounds in their compartmental structure. Many variants considered in the literature are computationally universal and/or able to solve NP-complete problems in polynomial (even linear) time — of course, by making use of an exponential working space created in a natural way (for instance, by membrane division).

In the present paper we propose a general class of membrane systems, where besides rules for objects evolution (the objects are described by strings over a finite alphabet), there are rules for moving objects from a compartment to another one (this is done conditionally, depending on the strings contents), and for handling membranes. Especially this latter feature is important (and new in many respects), because it makes possible to interpret several DNA computing experiments as membrane computations. Specifically, rules for dividing membranes (with the contents replicated or separated according to a given property of strings), creating, merging, or dissolving them are considered. Some of these variants generalize certain previous variants of membrane systems, for the new variants we investigate their power and computational efficiency (as expected, universality results, as well as polynomial solutions of NP-complete problems are found; the latter case is illustrated with the SAT problem).

Due to space restrictions, the paper is a preliminary, partially formalized one; more mathematical details are given in the appendices available at http://bioinformatics.bio.disco.unimib.it/psystems, where also current information about the membrane computing area can be found.