# Computing with Membranes

@article{Paun2000ComputingWM, title={Computing with Membranes}, author={Gheorghe Paun}, journal={J. Comput. Syst. Sci.}, year={2000}, volume={61}, pages={108-143} }

We introduce a new computability model, of a distributed parallel type, based on the notion of a membrane structure. Such a structure consists of several cell-like membranes, recurrently placed inside a unique “skin” membrane. A plane representation is a Venn diagram without intersected sets and with a unique superset. In the regions delimited by the membranes there are placed objects. These objects are assumed to evolve: each object can be transformed in other objects, can pass through a…

## 2,256 Citations

Computing with cells: membrane systems – some complexity issues

- Computer ScienceInt. J. Parallel Emergent Distributed Syst.
- 2008

Some interesting and fundamental complexity issues such as universality vs. nonuniversality, determinism vs. nondeterminism, membrane and alphabet size hierarchies, characterizations of context-sensitive languages and other language classes and various notions of parallelism are surveyed.

Computing with Membranes: Variants with an Enhanced Membrane Handling

- Computer ScienceDNA
- 2001

A general class of membrane systems, where besides rules for objects evolution, there are rules for moving objects from a compartment to another one, and for handling membranes, and this latter feature is important, because it makes possible to interpret several DNA computing experiments as membrane computations.

Membrane systems with limited parallelism

- Computer Science
- 2006

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 are introduced, which prove that these rewriting-symport P systems generate all recursively enumerable languages.

P Automata: Membrane Systems as Acceptors

- Computer ScienceCiE
- 2008

The concept of a membrane system (a P system) was introduced by Gheorghe Păun in 1998 with the aim of formulating a computational device abstracted from the architecture and the functioning of the living cell and has proved to be a successful area in bio-inspired computing.

Spatial Dynamic Structures and Mobility in Computation

- Computer ScienceArXiv
- 2011

This thesis addresses issues concerning the power of operations for modifying the membrane structure of a system of mobile membranes by mobility: endocytosis (moving a membrane inside a neighbouring membrane) and endocyTosis ( moving a membrane outside the membrane where it is placed).

Computing with membranes: P systems with worm-objects

- Computer Science, MathematicsProceedings Seventh International Symposium on String Processing and Information Retrieval. SPIRE 2000
- 2000

It is proved that P systems of this type can generate all recursively enumerable sets of numbers and the first time that a polynomial solution to an NP-complete problem has been obtained in the P system framework without making use of the (non-realistic) operation of membrane division.

## References

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It is shown that membrane division is not necessary in order to show that P systems with active membranes are computationally complete, and that HPP can be solved in polynomial time also by a variant of P systems, with the possibility of dividing non-elementary membranes under the influence of objects present in them.

Generalized P-Systems

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The model of generalized P-systems, GP- systems for short, is considered, a new model for computations using membrane structures and recently introduced by Gheorghe Păun, allowing for the simulation of graph controlled grammars of arbitrary type based on productions working on single objects.

On Synchronization in P Systems

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P Systems with Active Membranes: Attacking NP-Complete Problems

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It is proved that a class of P systems whose membranes are the main active components, in the sense that they directly mediate the evolution and the communication of objects, is not only computationally universal, but also able to solve NP complete problems in polynomial time.

On the Power of Membrane Computing

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- Computer Science, MathematicsWhere Mathematics, Computer Science, Linguistics and Biology Meet
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Characterizations of recursively enumerable languages are given, by means of splicing P systems, having splicing rules of small size (that is, involving short context strings), and it is shown that with only two membranes the authors can generate all the recursive enumerable Languages.