# Unexpected universality results for three classes of P systems with symport/antiport

- 40 Downloads
- 3 Citations

## Abstract

Symport and antiport are biological ways of transporting molecules through membranesin ``collaborating'' pairs; in the case of symport the two molecules pass in the same direction, in the case of antiport the two molecules pass in opposite directions. Here we first survey the results about the computing power of membrane systems (P systems) using only symport/antiport rules (hence these systems compute by communication only), then we consider a recently introduced, way of defining the result of a computation in a membrane system: looking for the trace of certain objects in their movement through membranes. Rather unexpected, in this way we get characterizations of recursively enumerable languages by means of membrane systems with symport/antiport which work with multisets of objects (note the qualitative difference between the data structure used by computations – multisets: no ordering– and the data structure of the output – strings: linear ordering). A similar remark holds true for the case of analysing P systems, which work in an automata-like manner: the sequence of certain distinguished objects taken from the environment during acomputation is the string recognized by the computation. We also survey universality results from this area, with sketched proofs. Some open problems are also formulated.

## Preview

Unable to display preview. Download preview PDF.

## References

- Alberts B et al. (1998) Essential cell biology. An introduction to the molecular biology of the cell. Garland Publ. Inc., New York, LondonGoogle Scholar
- Ardelean II (2002) The relevance of cell membranes for P systems. General aspects. Fundamenta Informaticae 49: 35–43zbMATHMathSciNetGoogle Scholar
- Csuhaj-Varju E and Vaszil G (2002) P automata. Pre-Proceedings of Workshop on Membrane Computing, Curtea de Argeş, Romania, 2002, MolCoNet Publication No. 1, pp. 177–192Google Scholar
- Freund R and Oswald M (2002) A short note on analysing P systems. Bulletin of the EATCS 78 (October 2002): 231–236MathSciNetGoogle Scholar
- Freund R and Păun Gh (2001) On the number of non-terminal symbols in graph-controlled, programmed and matrix grammars. In: Margenstern M and Rogozhin Y (eds) Proc. Conf. Universal Machines and Computations, Chişinău, 2001, LNCS 2055, pp. 214–225. Springer-VerlagGoogle Scholar
- Frisco P and Hoogeboom HJ (2002) Simulating counter automata by P systems with symport/antiport. Pre-Proceedings of Workshop on Membrane Computing, Curtea de Argeş, Romania, 2002, MolCoNet Publication No. 1, pp. 237–248Google Scholar
- Ionescu M. Martín-Vide C and Păun Gh (2002) P systems with symport/antiport rules: The traces of objects. Grammars 5: 65–79zbMATHMathSciNetCrossRefGoogle Scholar
- Martín-Vide C, Păun A and Păun Gh (2002) On the power of P systems with symport rules. Journal of Universal Computer Science 8: 317–331Google Scholar
- Martín-Vide C. Păaun A, Păun Gh and Rozenberg G (2002) Membrane systems with coupled transport: Universality and normal forms. Fundamenta Informaticae 49: 1–15zbMATHMathSciNetGoogle Scholar
- Martín-Vide C and Păun Gh (2001) Elements of Formal Language Theory for Membrane Computing. Technical Report 21/01 of the Research Group on Mathematical Linguistics, Rovira i Virgili University, TarragonaGoogle Scholar
- Păun A (2002) Membrane systems with symport/antiport: universality results. Pre-Proceedings of Workshop on Membrane Computing, Curtea de Argeş, Romania, 2002, MolCoNet Publication No. 1, pp. 333–343Google Scholar
- Păun A and Păun Gh (2002) The power of communication: P systems with symport/antiport. New Generation Computing 20: 295–306CrossRefzbMATHGoogle Scholar
- Păun A, Păun Gh and Rodriguez-Paton A (2001) Further remarks on P systems with symport rules. Ann. Univ. Al.I. Cuza, Iaşi 10: 3–18zbMATHGoogle Scholar
- Păun A, Păun Gh and Rozenberg G (2002) Computing by communication in networks of membranes. International Journal of Fundamentals of Computer Science 13: 779–798CrossRefzbMATHGoogle Scholar
- Păun Gh (2000) Computing with membranes. Journal of Computer and System Sciences 61: 108–143, and Turku Center for Computer Science-TUCS Report No. 208, 1998 (www.tucs.fi)MathSciNetCrossRefzbMATHGoogle Scholar
- Păun Gh (2002) Computing with Membranes: An Introduction. Springer-Verlag, BerlinGoogle Scholar
- Păun Gh, Rozenberg G and Salomaa A (2000) Membrane computing with external output. Fundamenta Informaticae 41: 259–266MathSciNetGoogle Scholar
- Sosik P (2002) P systems versus register machines: Two universality proofs. Pre-Proceedings of Workshop on Membrane Computing, Curtea de Argeş, Romania, 2002, MolCoNet Publication No. 1, pp. 371–382Google Scholar