# MASSIVE PARALLEL NETWORKS OF EVOLUTIONARY PROCESSORS AS NP-PROBLEM SOLVERS

### Nuria Gómez Blas, Luis F. de Mingo, Eugenio Santos

#### Abstract

This paper presents a new connectionist model that might be used to solve NP-problems. Most well known numeric models are Neural Networks that are able to approximate any function or classify any pattern set provided numeric information is injected into the net. Concerning symbolic information new research area has been developed, inspired by George Paun, called Membrane Systems. A step forward, in a similar Neural Network architecture, was done to obtain Networks of Evolutionary Processors (NEP). A NEP is a set of processors connected by a graph, each processor only deals with symbolic information using rules. In short, objects in processors can evolve and pass through processors until a stable configuration is reach. Despite their simplicity, we show how the latter networks might be used for solving an NP-complete problem, namely the 3-colorability problem, in linear time and linear resources (nodes, symbols, rules).

#### References

- Adleman, L. (1994). Molecular computation of solutions to combinatorial problems. Science, 226:1021-1024.
- Castellanos, J., de Mingo, L. F., and Mitrana, V. (2006). Solving sat by accepting networks of splicing processors with filtered connections. In 15th International Conference on Computing, pages 260-265.
- Castellanos, J., Martín-Vide, C., Mitrana, V., and Sempere, J. (2001). Solving np-complete problems with networks of evolutionary processors. Lecture Notes in Computer Science, 2084:621-628.
- Castellanos, J., Martín-Vide, C., Mitrana, V., and Sempere, J. (2003). Networks of evolutionary processors. Acta Informática, 39:517-529.
- Ciobanu, G., Paun, G., and Perez-Jimenez, M. (2005). Applications of Membrane Computing. Springer-Verlag, Berlin.
- Diaz, M., de Mingo, L., and Gómez, N. (2007). Networks of evolutionary processors: Java implementation of a threaded processor. International Conference on Information Research, Applications and Education - ITech'07, pages 203-210.
- Fahlman, S., Hinton, G., and Seijnowski, T. (1983). Massively parallel architectures for ai: Massively parallel architectures for ai: Netl, thistle and boltzmann machines. In AAAI National Conference on Artificial Intelligence, pages 109-113.

#### Paper Citation

#### in Harvard Style

Gómez Blas N., F. de Mingo L. and Santos E. (2008). **MASSIVE PARALLEL NETWORKS OF EVOLUTIONARY PROCESSORS AS NP-PROBLEM SOLVERS** . In *Proceedings of the Tenth International Conference on Enterprise Information Systems - Volume 2: ICEIS,* ISBN 978-989-8111-37-1, pages 588-592. DOI: 10.5220/0001721405880592

#### in Bibtex Style

@conference{iceis08,

author={Nuria Gómez Blas and Luis F. de Mingo and Eugenio Santos},

title={MASSIVE PARALLEL NETWORKS OF EVOLUTIONARY PROCESSORS AS NP-PROBLEM SOLVERS},

booktitle={Proceedings of the Tenth International Conference on Enterprise Information Systems - Volume 2: ICEIS,},

year={2008},

pages={588-592},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001721405880592},

isbn={978-989-8111-37-1},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Tenth International Conference on Enterprise Information Systems - Volume 2: ICEIS,

TI - MASSIVE PARALLEL NETWORKS OF EVOLUTIONARY PROCESSORS AS NP-PROBLEM SOLVERS

SN - 978-989-8111-37-1

AU - Gómez Blas N.

AU - F. de Mingo L.

AU - Santos E.

PY - 2008

SP - 588

EP - 592

DO - 10.5220/0001721405880592