Autonomous Resolution Based on DNA Strand Displacement
We present a computing model based on the technique of DNA strand displacement which performs a chain of logical resolutions with logical formulae in conjunctive normal form. The model is enzyme-free and autonomous. Each clause of a formula is encoded in a separate DNA molecule: propositions are encoded assigning a strand to each proposition p, and its complementary strand to the proposition ¬p; clauses are encoded comprising different propositions in the same strand. The model allows to run logic programs composed of Horn clauses by cascading resolution steps and, therefore, possibly function as an autonomous programmable nano-device. This technique can be also used to solve SAT. The resulting SAT algorithm has a linear time complexity in the number of resolution steps, whereas its spatial complexity is exponential in the number of variables of the formula.
KeywordsConjunctive Normal Form Logical Formula Horn Clause Strand Displacement Resolution Step
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