A comparison of resource-bounded molecular computation models

The number of molecular strands used by a molecular algorithm is an importa nt measure of the algorithm's complexity. This measure is also called the v olume used by the algorithm. We prove that three important polynomial-time models of molecular computation with bounded volume are equivalent to model s of polynomial-time Turing machine computation with bounded nondeterminism . Without any assumption, we show that the Split operation does not increas e the power of polynomial-time molecular computation. Assuming a plausible separation between Turing machine complexity classes, the Amplify operation does increase the power of polynomial-time molecular computation.