Abstract
The number of molecular strands used by a molecular algorithm is an important measure of the algorithm's complexity. This measure is also called the volume used by the algorithm. We prove that three important polynomial-time models of molecular computation with bounded volume are equivalent to models of polynomial-time Turing machine computation with bounded nondeterminism. Without any assumption, we show that the Split operation does not increase 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.
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