Abstract
Speed of computation and power consumption are the two main parameters of conventional computing devices implemented in microelectronic circuits. As performance of such devices approaches physical limits, new computing paradigms are emerging. Two paradigms receiving great attention are quantum and DNA-based molecular computing. This paper focuses on DNA-based computing. This paradigm can be abstracted to growth models where computational elements called tiles are self-assembled one by one, subject to some simple hierarchical rules, to fill a given template encoding a Boolean formula. While DNA-based computational devices are known to be extremely energy efficient, little is known concerning the fundamental question of computation times. In particular, given a function, we study the time required to determine its value for a given input. In the simplest instance, the analysis has interesting connections with interacting particle systems and variational problems. © Springer-Verlag Berlin Heidelberg 2005.