A scalable approach to DNA-based computations is described. Complex co
mbinatorial mixtures of DNA molecules encoding all possible answers to
a computational problem are synthesized and attached to the surface o
f a solid support. This set of molecules is queried in successive MARK
(hybridization) and DESTROY (enzymatic digestion) operations. Determi
nation of the sequence of the DNA molecules remaining on the surface a
fter completion of these operations yields the answer to the computati
onal problem. Experimental demonstrations of aspects of the strategy a
re presented.