An improved DNA-sticker addition algorithm and its application to logarithmic arithmetic

  • Authors:
  • Mark G. Arnold

  • Affiliations:
  • Lehigh University, Bethlehem, PA

  • Venue:
  • DNA'11 Proceedings of the 17th international conference on DNA computing and molecular programming
  • Year:
  • 2011

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Abstract

The sticker model of computation, implemented using robotic processing of DNA, manipulates in parallel many bitstrings, called strands, that are contained in a limited number of tubes. Prior sticker-addition algorithms are patterned on digital-electronic full-adders that generate carry bits, each of which must be saved in the strand, which involves wasting the strand or using a clear operation (whose biochemical implementation may be problematic). This paper proposes a new sticker-addition algorithm which does not need to record the carry bits. Instead, which tube holds a particular strand implicitly describes whether or not a carry is required. The speed and number of tubes needed are about half that needed by the prior approach. An example is given for real-valued Euclidian norms using the Logarithmic Number System.