Constant-Size Tileset for Solving an NP-Complete Problem in Nondeterministic Linear Time

  • Yuriy Brun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4848)

Abstract

The tile assembly model, a formal model of crystal growth, is of special interest to computer scientists and mathematicians because it is universal [1]. Therefore, tile assembly model systems can compute all the functions that computers compute. In this paper, I formally define what it means for a system to nondeterministically decide a set, and present a system that solves an NP-complete problem called SubsetSum. Because of the nature of NP-complete problems, this system can be used to solve all NP problems in polynomial time, with high probability. While the proof that the tile assembly model is universal [2] implies the construction of such systems, those systems are in some sense “large” and “slow.” The system presented here uses 49 = Θ(1) different tiles and computes in time linear in the input size. I also propose how such systems can be leveraged to program large distributed software systems.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Yuriy Brun
    • 1
  1. 1.Department of Computer ScienceUniversity of Southern CaliforniaLos Angeles 

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