Theoretical and Experimental DNA Computation (Natural ...

136 5 Physical Implementations
5.9.1 Chess Games
In [58], Faulhammer et al. describe a solution to a variant of the satisfiability
problem that uses RNA rather than DNA as the computational substrate.
They consider a variant of SAT, the so-called “Knight problem”, which seeks
configurations of knights on an n × n chess board, such that no knight is
attacking any other. Examples of legal and illegal configurations are depicted
in Fig. 5.13.
(a) (b)
Fig. 5.13. (a) Legal configuration. (b) Illegal configuration - both knights can attack
one another
In keeping with our earlier observations, the authors prefer a “mark and destroy”
strategy [12] rather than the repeated use of hybridization extraction
to remove illegal solutions. However, the use of an RNA library and ribonuclease
(RNase) H digestion gives greater flexibility, as one is not constrained
by the set of restriction enzymes available. In this way, the RNase H acts as
a “universal restriction enzyme”, allowing selective marking of virtually any
RNA strands for parallel destruction by digestion.
The particular instance solved in [58] used a 3×3 board, with the variables
a−i representing the squares (Fig. 5.14). If a variable is set to 1 then a knight
is present at that variable’s square, and 0 represents the absence of a knight.
a b c
d e f
g h i
Fig. 5.14. Labelling of test board
The 3 × 3 knight problem may therefore be represented as the following instance
of SAT: