LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

The Power of Networks of Watson-Crick D0L
Systems
Erzsébet Csuhaj-Varjú 1 and Arto Salomaa 2
1 Computer and Automation Research Institute
Hungarian Academy of Sciences
Kende u. 13-17
H-1111 Budapest, Hungary
csuhaj@sztaki.hu
2 Turku Centre for Computer Science
Lemminkäisenkatu 14 A
FIN -20520 Turku, Finland
asalomaa@it.utu.fi
Abstract. The notion of a network of Watson-Crick D0L systems was
recently introduced, [7]. It is a distributed system of deterministic language
defining devices making use of Watson-Crick complementarity.
The research is continued in this paper, where we establish three results
about the power of such networks. Two of them show how it is
possible to solve in linear time two well-known NP-complete problems,
the Hamiltonian Path Problem and the Satisfiability Problem. Here the
characteristic feature of DNA computing, the massive parallelism, is used
very strongly. As an illustration we use the propositional formula from
the celebrated recent paper, [3]. The third one shows how in the very
simple case of four-letter DNA alphabets we can obtain weird (not even
Z-rational) patterns of population growth.
1 Introduction
Many mathematical models of DNA computing have been investigated, some
of them already before the fundamental paper of Adleman, [1]. The reader is
referred to [11,2] for details. Networks of language generating devices, in the
sense investigated in this paper, were introduced in [5,6,7]. This paper continues
the work begun in [7]. The underlying notion of a Watson-Crick D0L system was
introduced and studied further in [10,8,16,17,18,20,4].
The reader can find background material and motivation in the cited references.
Technically this paper is largely self-contained. Whenever need arises,
[14,13] can be consulted in general matters about formal languages, [12] in matters
dealing with Lindenmayer systems, and [19,9] in matters dealing with formal
power series.
Watson-Crick complementarity is a fundamental concept in DNA computing.
A notion, called Watson-Crick D0L system, where the paradigm of complementarity
is considered in the operational sense, was introduced in [10].
N. Jonoska et al. (Eds.): Molecular Computing (Head Festschrift), LNCS 2950, pp. 106–118, 2004.
c○ Springer-Verlag Berlin Heidelberg 2004