DNA-based algorithms for learning Boolean formulae

We apply a DNA-based massively parallel exhaustive search to solving the computational learning problems of DNF (disjunctive normal form) Boolean formulae. Learning DNF formulae from examples is one of the most important open problems in computational learning theory and the problem of learning 3-term DNF formulae is known as intractable if RP ≠ NP. We propose new methods to encode any k-term DNF formula to a DNA strand, evaluate the encoded DNF formula for a truth-value assignment by using hybridization and primer extension with DNA polymerase, and find a consistent DNF formula with the given examples. By employing these methods, we show that the class of k-term DNF formulae (for any constant k) and the class of general DNF formulae are efficiently learnable on DNA computer. Second, in order for the DNA-based learning algorithm to be robust for errors in the data, we implement the weighted majority algorithm on DNA computers, called DNA-based majority algorithm via amplification (DNAMA), which take a strategy of "amplifying" the consistent (correct) DNA strands. We show a theoretical analysis for the mistake bound of the DNA-based majority algorithm via amplification, and imply that the amplification to "double the volumes" of the correct DNA strands in the test tube works well.