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 2b(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.
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