Spiking neural P systems with extended rules: universality and languages
- 120 Downloads
We consider spiking neural P systems with rules allowed to introduce zero, one, or more spikes at the same time. The motivation comes both from constructing small universal systems and from generating strings; previous results from these areas are briefly recalled. Then, the computing power of the obtained systems is investigated, when considering them as number generating and as language generating devices. In the first case, a simpler proof of universality is obtained, while in the latter case we find characterizations of finite and recursively enumerable languages (without using any squeezing mechanism, as it was necessary in the case of standard rules). The relationships with regular languages are also investigated.
KeywordsMembrane computing Spiking neural P systems Turing computability Universality Chomsky hierarchy
Unable to display preview. Download preview PDF.
The authors gratefully acknowledge the following (partial) support of their research. H. Chen: Grants numbers 60573013 and 60421001 of the National Natural Science Foundation of China. M. Ionescu: Programa Nacional para la Formación del Profesorado Universitario from the Spanish Ministry of Education. A. Păun: LA BoR RSC grant LEQSF (2004-07)-RD-A-23, and NSF Grants IMR-0414903 and CCF-0523572. Gh. Păun and M.J. Pérez-Jiménez: Project TIN2005-09345-C03-01 of Ministerio de Educación y Ciencia of Spain, cofinanced by FEDER funds, and Project of Excellence TIC 581 of Junta de Andalucia.
- Chen H, Freund R, Ionescu M, Păun Gh, Pérez-Jiménez MJ (2006) On string languages generated by spiking neural P systems. In Proceedings of the fourth brainstorming week on membrane computing, vol. I, Sevilla, pp 169–193 (available at http://psystems.disco.unimib.it)
- Ibarra OH, Păun A, Păun Gh, Rodrí guez-Patón A, Sosik P, Woodworth S (2006) Normal forms for spiking neural P systems. In Fourth brainstorming week on membrane computing, Febr. 2006, vol. II, Fenix Editora, Sevilla, pp 105–136Google Scholar
- Maass W (2002) Computing with spikes. Special Issue Found Inform Process TELEMATIK 8(1):32–36Google Scholar
- Maass W, Bishop C (eds) (1999) Pulsed neural networks. MIT Press, CambridgeGoogle Scholar
- Păun Gh (2002) Membrane computing – an introduction. Springer-Verlag, BerlinGoogle Scholar
- Păun A, Păun Gh (to appear) Small universal spiking neural P systems. BioSystemsGoogle Scholar
- Rozenberg G, Salomaa A (eds) (1997) Handbook of formal languages, 3 volumes. Springer-Verlag, BerlinGoogle Scholar
- The P Systems Web Page: http://psystems.disco.unimib.it