Self-assembly of Decidable Sets

Authors:
Matthew J. Patitz;Scott M. Summers
Affiliations:
Department of Computer Science, Iowa State University, Ames, U.S.A. IA 50011;Department of Computer Science, Iowa State University, Ames, U.S.A. IA 50011
Venue:
UC '08 Proceedings of the 7th international conference on Unconventional Computing
Year:
2008

Citing 6
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Abstract

The theme of this paper is computation in Winfree's Abstract Tile Assembly Model (TAM). We first review a simple, well-known tile assembly system (the "wedge construction") that is capable of universal computation. We then extend the wedge construction to prove the following result: if a set of natural numbers is decidable, then it and its complement's canonical two-dimensional representation self-assemble. This leads to a novel characterization of decidable sets of natural numbers in terms of self-assembly. Finally, we prove that our construction is, in some "natural" sense, optimal with respect to the amount of space it uses.