LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

150 Franziska Freund, Rudolf Freund, and Marion Oswald
1. for r being of the form Au1#v1B$u2#v2, i= k for or2 = in and i = l for
or2 = out,
2. for r being of the form u1#v1$Au2#v2B, i= k for or1 = in and i = l for
or1 = out.
The construction elaborated above proves that for every membrane system
with splicing rules assigned to membranes we can effectively construct an equivalent
test tube system communicating by splicing.
As the results in this section show, membrane systems with splicing rules
assigned to membranes are eqivalent to the variants of test tube systems using
splicing rules that we considered in the previous section, and therefore they have
universal computational power (also see [9]), too.
5 Summary and Related Results
In this paper we have shown that splicing test tube systems and the new variant
of test tube systems communicating by splicing are equivalent to (sequential)
P systems using splicing rules assigned to membranes. Although using quite
restricted variants of splicing rules on end-marked strings, all the systems considered
in this paper have universal computational power, which results already
follow from results obtained previously.
For splicing test tube systems, the results proved in [7] show that two test
tubes are enough for obtaining universal computational power, which result is
optimal with respect to the number of tubes. For P systems using splicing rules
assigned to membranes, the results proved in [9] (there the environment played
the rôle of the region enclosed by the skin membrane) show that (with respect
to the definitions used in this paper) two membranes are enough, which result
then is optimal with respect to the number of membranes. On the other hand,
the number of test tubes in the new variant of test tube systems communicating
by splicing cannot be bounded.
Acknowledgements
We gratefully acknowledge many interesting and fruitful discussions on splicing
and DNA computing with Tom Head.
References
1. L.M. Adleman, Molecular computation of solutions to combinatorial problems,
Science, 226 (1994), 1021–1024.
2. E. Csuhaj-Varjú, L. Kari, Gh. Păun, Test tube distributed systems based on splicing,
Computers and Artificial Intelligence, 15, 2 (1996), 211–232.
3. J. Dassow, Gh. Păun, On the power of membrane computing, Journal of Universal
Computer Science 5, 2 (1999), 33–49 (http://www.iicm.edu/jucs).