**Authors:**
Richard Beigel and Bin Fu

**Abstract:** The maximum number of strands used is an important
measure of a molecular algorithm's complexity. This measure is also
called the space used by the algorithm. We show that every NP problem
that can be solved with *b*(*n*) bits of nondeterminism can
be solved by molecular computation in a polynomial number of steps,
with four test tubes, in space 2^{b(n)}. In
addition, we identify a large class of recursive algorithms that can
be implemented using bounded nondeterminism. This yields improved
molecular algorithms for important problems like 3-SAT, independent
set, and 3-colorability.