Complexity of Compact Proofreading for Self-assembled Patterns

  • David Soloveichik
  • Erik Winfree
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3892)


Fault-tolerance is a critical issue for biochemical computation. Recent theoretical work on algorithmic self-assembly has shown that error correcting tile sets are possible, and that they can achieve exponential decrease in error rates with a small increase in the number of tile types and the scale of the construction [24, 4]. Following [17], we consider the issue of applying similar schemes to achieve error correction without any increase in the scale of the assembled pattern. Using a new proofreading transformation, we show that compact proofreading can be performed for some patterns with a modest increase in the number of tile types. Other patterns appear to require an exponential number of tile types. A simple property of existing proofreading schemes – a strong kind of redundancy – is the culprit, suggesting that if general purpose compact proofreading schemes are to be found, this type of redundancy must be avoided.


Tile System Block Type Bond Type Tile Type Quarter Plane 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • David Soloveichik
    • 1
  • Erik Winfree
    • 1
  1. 1.Department of CNS and CSCalifornia Institute of TechnologyUSA

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