Counting DNA: estimating the complexity of a test tube of DNA

We consider the problem of estimation of the `complexityʹ of a test tube of DNA. The complexity of a test tube is the number of different kinds of strands of DNA in the test tube. It is quite easy to estimate the number of total strands in a test tube, especially if the strands are all the same length. Estimation of the complexity is much less clear. We propose a simple kind of DNA computation that can estimate the complexity.