LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

Plasmids to Solve #3SAT
Rani Siromoney 1 and Bireswar Das 2
1 Madras Christian College
Chennai 600 059, India, and
Chennai Mathematical Institute
Chennai 600 017, India
ranisiro@sify.com
2 Institute of Mathematical Sciences
Chennai 600 113, India
bireswar@imsc.res.in
Abstract. Tom Head, [1] has given a simple and elegant method of
aqueous computing to solve 3SAT. The procedure makes use of Divide-
Delete-Drop operations performed on plasmids. In [4], a different set of
operations, Cut-Expand-Ligate, are used to solve several NP-Complete
problems. In this paper, we combine the features in the two procedures
and define Cut-Delete-Expand-Ligate which is powerful enough to solve
#3SAT, which is a counting version of 3SAT known to be in IP. The
solution obtained is advantageous to break the propositional logic based
cryptosystem introduced by J. Kari [5].
1 Plasmids for Aqueous Computing
DNA molecules occur in nature in both linear and circular form. Plasmids are
small circular double-stranded DNA molecules. They carry adequate information
encoded in their sequences necessary for their replication and this is used in
genetic engineering. The technique used is cut and paste – cutting by restriction
enzymes and pasting by a ligase. The sequential application of a set of restriction
enzymes acting at distinct non-overlapping, different sites in circular DNA
molecules is fundamental to the procedure suggested below.
2 Divide-Delete-Drop (D-D-D)
Tom Head [1] has given the following procedure which provides the correct
YES/NO answer for instances of 3-SAT in a number of steps linearly bounded
by the sum of the number of atomic propositional variables and the number of
triples that are disjoined.
The fundamental data structure for the computational work involved in D-
D-D is an artificial plasmid constructed as follows.
For a specified set of restriction enzymes {RE1,RE2,...,REn}, the plasmid
contains a segment of the form c1s1c1c2s2c2 ...cisici ...cn−1sn−1cn−1cnsncn;
the subsegments c1,c2,...,cn are sites at which the enzymes RE1,...,REn can
N. Jonoska et al. (Eds.): Molecular Computing (Head Festschrift), LNCS 2950, pp. 361–366, 2004.
c○ Springer-Verlag Berlin Heidelberg 2004