LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

154 Max H. Garzon, Kiranchand V. Bobba, and Bryan P. Hyde
approximation models [8]. Hence an exhaustive search of strands sets of words
maximally separated in a given coding space is infeasible, even for the small
oligo-nucleotides useful in DNA computing.
To cope with this problem, a much simpler and computationally tractable
model, the h-distance, was introduced in [18]. Here, we show how an abstraction
of this concept to include binary strings can be used to produce code sets
of high enough quality for use in vitro, i.e., how to encode symbolic information
in biomolecules for robust and fault-tolerant computing. By introducing a
DNA-like structure into binary data, one expects to introduce good properties
of DNA into electronic information processing while retaining good properties
of electronic data storage and processing (such as programmability and reliability).
In this section it is shown how to associate basic DNA-like properties with
binary strings, and in the remaining sections we show how to use good coding
sets in binary with respect to this structure to obtain good codeword sets for
computing with biomolecules in vitro.
2.1 Binary DNA
Basic features of DNA structure can be brought into data representations traditionally
used in conventional computing as follows. Information is usually represented
in binary strings, butthey are treated them as analogs of DNA strands,
and refer to them as binary oligomers, or simply biners. The pseudo-base (or abstract
base) 0 binds with 1, and vice versa, to create a complementary pair 0/1,
in analogy with Watson-Crick bonding of natural nucleic bases. These concepts
can be extended to biners recursively as follows
(xa) R := y R x R , and(xa) wc := a wc x wc , (1)
where the superscripts R and wc stand for the reversal operation and the Watson-
Crick complementary operation, respectively. The resulting single and double
strands are referred to as binary DNA, orsimplyBNA. Hybridization of single
DNA strands is of crucial importance in biomolecular computing and it thus
needs to be defined properly for BNA. The motivation is, of course, the analogous
ensemble processes with DNA strands [30].
2.2 h-Distance
A measure of hybridization likelihood between two DNA strands has been introduced
in [18]. A similar concept can be used in the context of BNA. The
h-measure between two biners x, y is given by
|x, y| := min
−n