Date of Award

Fall 2006

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Computational Analysis and Modeling

First Advisor

Andrei Paun

Abstract

Membrane computing is an emerging research field that belongs to the more general area of molecular computing, which deals with computational models inspired from bio-molecular processes. Membrane computing aims at defining models, called membrane systems or P systems, which abstract the functioning and structure of the cell. A membrane system consists of a hierarchical arrangement of membranes delimiting regions, which represent various compartments of a cell, and with each region containing bio-chemical elements of various types and having associated evolution rules, which represent bio-chemical processes taking place inside the cell.

This work is a continuation of the investigations aiming to bridge membrane computing (where in a compartmental cell-like structure the chemicals to evolve are placed in compartments defined by membranes) and brane calculi (where one considers again a compartmental cell-like structure with the chemicals/proteins placed on the membranes themselves). We use objects both in compartments and on membranes (the latter are called proteins), with the objects from membranes evolving under the control of the proteins. Several possibilities are considered (objects only moved across membranes or also changed during this operation, with the proteins only assisting the move/change or also changing themselves). Somewhat expected, computational universality is obtained for several combinations of such possibilities.

We also present a method for solving the NP-complete SAT problem using P systems with proteins on membranes. The SAT problem is solved in O(nm) time, where n is the number of boolean variables and m is the number of clauses for an instance written in conjunctive normal form. Thus, we can say that the solution for each given instance is obtained in linear time. We succeeded in solving SAT by a uniform construction of a deterministic P system which uses rules involving objects in regions, proteins on membranes, and membrane division.

Then, we investigate the computational power of P systems with proteins on membranes in some particular cases: when only one protein is placed on a membrane, when the systems have a minimal number of rules, when the computation evolves in accepting or computing mode, etc.

This dissertation introduces also another new variant of membrane systems that uses context-free rewriting rules for the evolution of objects placed inside compartments of a cell, and symport rules for communication between membranes. The strings circulate across membranes depending on their membership to regular languages given by means of regular expressions. We prove that these rewriting-symport P systems generate all recursively enumerable languages. We investigate the computational power of these newly introduced P systems for three particular forms of the regular expressions that are used by the symport rules. A characterization of ET0L languages is obtained in this context.

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