Abstract
This paper answers an open question of Chen, Doty, and Soloveichik [5], who showed that a function f:ℕk → ℕl is deterministically computable by a stochastic chemical reaction network (CRN) if and only if the graph of f is a semilinear subset of ℕk + l. That construction crucially used “leaders”: the ability to start in an initial configuration with constant but non-zero counts of species other than the k species X 1,…,X k representing the input to the function f. The authors asked whether deterministic CRNs without a leader retain the same power.
We answer this question affirmatively, showing that every semilinear function is deterministically computable by a CRN whose initial configuration contains only the input species X 1,…,X k , and zero counts of every other species. We show that this CRN completes in expected time O(n), where n is the total number of input molecules. This time bound is slower than the O(log5 n) achieved in [5], but faster than the O(n logn) achieved by the direct construction of [5].
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-3-319-01928-4_15
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References
Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M., Peralta, R.: Computation in networks of passively mobile finite-state sensors. Distributed Computing 18, 235–253 (2006); Preliminary version appeared in PODC 2004
Angluin, D., Aspnes, J., Eisenstat, D.: Stably computable predicates are semilinear. In: PODC 2006: Proceedings of the Twenty-fifth Annual ACM Symposium on Principles of Distributed Computing, pp. 292–299. ACM Press, New York (2006)
Angluin, D., Aspnes, J., Eisenstat, D.: Fast computation by population protocols with a leader. In: Dolev, S. (ed.) DISC 2006. LNCS, vol. 4167, pp. 61–75. Springer, Heidelberg (2006)
Cardelli, L.: Strand algebras for DNA computing. Natural Computing 10(1), 407–428 (2011)
Chen, H.-L., Doty, D., Soloveichik, D.: Deterministic function computation with chemical reaction networks. In: Stefanovic, D., Turberfield, A. (eds.) DNA 18. LNCS, vol. 7433, pp. 25–42. Springer, Heidelberg (2012)
Condon, A., Hu, A., Maňuch, J., Thachuk, C.: Less haste, less waste: On recycling and its limits in strand displacement systems. Journal of the Royal Society Interface 2, 512–521 (2012); In: Cardelli, L., Shih, W. (eds.) DNA 17. LNCS, vol. 6937, pp. 84–99. Springer, Heidelberg (2011)
Condon, A., Kirkpatrick, B., Maňuch, J.: Reachability bounds for chemical reaction networks and strand displacement systems. In: Stefanovic, D., Turberfield, A. (eds.) DNA 18. LNCS, vol. 7433, pp. 43–57. Springer, Heidelberg (2012)
Cook, M., Soloveichik, D., Winfree, E., Bruck, J.: Programmability of chemical reaction networks. In: Condon, A., Harel, D., Kok, J.N., Salomaa, A., Winfree, E. (eds.) Algorithmic Bioprocesses, pp. 543–584. Springer, Heidelberg (2009)
Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry 81(25), 2340–2361 (1977)
Hjelmfelt, A., Weinberger, E.D., Ross, J.: Chemical implementation of neural networks and Turing machines. Proceedings of the National Academy of Sciences 88(24), 10983–10987 (1991)
Jiang, H., Riedel, M., Parhi, K.: Digital signal processing with molecular reactions. IEEE Design and Test of Computers 29(3), 21–31 (2012)
Magnasco, M.O.: Chemical kinetics is Turing universal. Physical Review Letters 78(6), 1190–1193 (1997)
Soloveichik, D.: Robust stochastic chemical reaction networks and bounded tau-leaping. Journal of Computational Biology 16(3), 501–522 (2009)
Soloveichik, D., Cook, M., Winfree, E., Bruck, J.: Computation with finite stochastic chemical reaction networks. Natural Computing 7(4), 615–633 (2008)
Thachuk, C., Condon, A.: Space and energy efficient computation with DNA strand displacement systems. In: Stefanovic, D., Turberfield, A. (eds.) DNA 18. LNCS, vol. 7433, pp. 135–149. Springer, Heidelberg (2012)
Zavattaro, G., Cardelli, L.: Termination problems in chemical kinetics. In: van Breugel, F., Chechik, M. (eds.) CONCUR 2008. LNCS, vol. 5201, pp. 477–491. Springer, Heidelberg (2008)
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Doty, D., Hajiaghayi, M. (2013). Leaderless Deterministic Chemical Reaction Networks. In: Soloveichik, D., Yurke, B. (eds) DNA Computing and Molecular Programming. DNA 2013. Lecture Notes in Computer Science, vol 8141. Springer, Cham. https://doi.org/10.1007/978-3-319-01928-4_4
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DOI: https://doi.org/10.1007/978-3-319-01928-4_4
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