DNA displacement reaction and its applications in constructing logical systems. A) Scheme of a three-input majority gate based on toehold-mediated DNA strand displacement reactions (reprinted by permission from reference [8], copyright 2013, American Chemical Society). B) Abstract diagram for a square-root circuit implemented with the logical DNA motif based on toehold-exchange DNA strand displacement reactions (from reference [12], reprinted with permission from AAAS). C) Scheme of programming chemical reactions using short single strands of DNA (reprinted by permission from reference [13], Macmillan Publishers Ltd., Nat. Nanotechnol., copyright 2013).