The computational power of Benenson automata

The development of autonomous molecular computers capable of making independent decisions in vivo regarding local drug administration may revolutionize medical science. Recently Benenson et al. [An autonomous molecular computer for logical control of gene expression, Nature 429 (2004) 423-429.] have envisioned one form such a “smart drug” may take by implementing an in vitro scheme, in which a long DNA state molecule is cut repeatedly by a restriction enzyme in a manner dependent upon the presence of particular short DNA “rule molecules.” To analyze the potential of their scheme in terms of the kinds of computations it can perform, we study an abstraction assuming that a certain class of restriction enzymes is available and reactions occur without error. We also discuss how our molecular algorithms could perform with known restriction enzymes. By exhibiting a way to simulate arbitrary circuits, we show that these “Benenson automata” are capable of computing arbitrary Boolean functions. Further, we show that they are able to compute efficiently exactly those functions computable by log-depth circuits. Computationally, we formalize a new variant of limited width branching programs with a molecular implementation.