Abstract
This paper explores the use of negative (i.e., repulsive) interactions in the abstract Tile Assembly Model defined by Winfree. Winfree in his Ph.D. thesis postulated negative interactions to be physically plausible, and Reif, Sahu, and Yin studied them in the context of reversible attachment operations. We investigate the power of negative interactions with irreversible attachments, and we achieve two main results. Our first result is an impossibility theorem: after t steps of assembly, Ω(t) tiles will be forever bound to an assembly, unable to detach. Thus negative glue strengths do not afford unlimited power to reuse tiles. Our second result is a positive one: we construct a set of tiles that can simulate an s-space-bounded, t-time-bounded Turing machine, while ensuring that no intermediate assembly grows larger than O(s), rather than O(s ·t) as required by the standard Turing machine simulation with tiles.
This research was supported in part by Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant R2824A01 and the Canada Research Chair Award in Biocomputing to Lila Kari, and by the NSF Computing Innovation Fellowship grant to David Doty.
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Doty, D., Kari, L., Masson, B. (2011). Negative Interactions in Irreversible Self-assembly. In: Sakakibara, Y., Mi, Y. (eds) DNA Computing and Molecular Programming. DNA 2010. Lecture Notes in Computer Science, vol 6518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18305-8_4
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DOI: https://doi.org/10.1007/978-3-642-18305-8_4
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