**Authors:** Bin Fu and Richard Beigel

**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.