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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aggarwal, G., Cheng, Q., Goldwasser, M.H., Kao, M.-Y., Moisset de Espanés, P., Schweller, R.T.: Complexities for generalized models of self-assembly. SIAM Journal on Computing 34, 1493–1515 (2005); Preliminary version appeared in SODA 2004
Doty, D., Lutz, J.H., Patitz, M.J., Summers, S.M., Woods, D.: Random number selection in self-assembly. In: Calude, C.S., Costa, J.F., Dershowitz, N., Freire, E., Rozenberg, G. (eds.) UC 2009. LNCS, vol. 5715, pp. 143–157. Springer, Heidelberg (2009)
Doty, D., Lutz, J.H., Patitz, M.J., Summers, S.M., Woods, D.: Intrinsic universality in self-assembly. In: STACS 2010: Proceedings of the 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), vol. 5, pp. 275–286 (2010)
Reif, J.H., Sahu, S., Yin, P.: Complexity of graph self-assembly in accretive systems and self-destructible systems. In: Carbone, A., Pierce, N.A. (eds.) DNA 11. LNCS, vol. 3892, pp. 257–274. Springer, Heidelberg (2006)
Rothemund, P.W.K., Winfree, E.: The program-size complexity of self-assembled squares (extended abstract). In: STOC 2000: Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing, pp. 459–468 (2000)
Schoen, R., Yau, S.-T.: On the positive mass conjecture in general relativity. Communications in Mathematical Physics 65(45), 45–76 (1979)
Seeman, N.C.: Nucleic-acid junctions and lattices. Journal of Theoretical Biology 99, 237–247 (1982)
Soloveichik, D., Cook, M., Winfree, E., Bruck, J.: Computation with finite stochastic chemical reaction networks. Natural Computing 7(4), 615–633 (2008)
Wang, H.: Proving theorems by pattern recognition – II. The Bell System Technical Journal XL(1), 1–41 (1961)
Winfree, E.: Algorithmic Self-Assembly of DNA. PhD thesis, California Institute of Technology (June 1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-18305-8_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-18304-1
Online ISBN: 978-3-642-18305-8
eBook Packages: Computer ScienceComputer Science (R0)