The bounded complexity of DNA computing

This paper proposes a new approach to analyzing DNA-based algorithms in molecular computation. Such protocols are characterized abstractly by: encoding, tube operations and extraction. Implementation of these approaches involves encoding in a multiset of molecules that are assembled in a tube having a number of physical attributes. The physico-chemical state of a tube can be changed by a prescribed number of elementary operations. Based on realistic definitions of these elementary operations, we define complexity of a DNA-based algorithm using the physico-chemical property of each operation. We show that new algorithms for Hamiltonian path are about twice as efficient as Adleman's original one and that a recent algorithm for Max-Clique provides a similar increase in efficiency. Consequences of this approach to tube complexity and DNA computing are discussed.