Molecular Computing, Bounded Nondeterminism, and Efficient Recursion

The maximum number of strands used is an important measure of a molecular algorithm's complexity. This measure is also called the volume used by the algorithm. Every problem that can be solved by an NP Turing machine with b(n) binary nondeterministic choices can be solved by molecular computation in a polynomial number of steps, with four test tubes, in volume 2 ^b(n) . 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. Received May 5, 1997; revised March 24, 1998.