Abstract
We demonstrate how the DSD programming language can be used to design a DNA stack machine and to analyse its behaviour. Stack machines are of interest because they can efficiently simulate a Turing machine. We extend the semantics of the DSD language to support operations on DNA polymers and use our stack machine design to implement a non-trivial example: a ripple carry adder which can sum two binary numbers of arbitrary size. We use model checking to verify that the ripple carry adder executes correctly on a range of inputs. This provides the first opportunity to assess the correctness and kinetic properties of DNA strand displacement systems performing Turing-powerful symbolic computation.
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.
Similar content being viewed by others
References
Venkataraman, S., Dirks, R.M., Ueda, C.T., Pierce, N.A.: Selective cell death mediated by small conditional RNAs. Proc. Natl. Acad. Sci. U S A 107(39), 16777–16782 (2010)
Turing, A.M.: On computable numbers, with an application to the Entscheidungsproblem. Proc. London Mathematical Society s2-42(1), 230–265 (1937)
Zhang, D.Y., Seelig, G.: Dynamic DNA nanotechnology using strand-displacement reactions. Nat. Chem. 3, 103–113 (2011)
Qian, L., Soloveichik, D., Winfree, E.: Efficient turing-universal computation with DNA polymers. In: Sakakibara, Y., Mi, Y. (eds.) DNA 16 2010. LNCS, vol. 6518, pp. 123–140. Springer, Heidelberg (2011)
Phillips, A., Cardelli, L.: A programming language for composable DNA circuits. J. R. Soc. Interface 6(suppl 4), S419–S436 (2009)
Paulevé, L., Youssef, S., Lakin, M.R., Phillips, A.: A generic abstract machine for stochastic process calculi. In: Proc. CMSB 2010, pp. 43–54. ACM, New York (2010)
Zhang, D.Y.: Towards domain-based sequence design for DNA strand displacement reactions. In: Sakakibara, Y., Mi, Y. (eds.) DNA 16 2010. LNCS, vol. 6518, pp. 162–175. Springer, Heidelberg (2011)
Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 115, 1716–1733 (2001)
Hinton, A., Kwiatkowska, M., Norman, G., Parker, D.: PRISM: A tool for automatic verification of probabilistic systems. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 441–444. Springer, Heidelberg (2006)
Bennett, C.H.: The thermodynamics of computation—a review. Int. J. Theor. Phys. 21(12), 905–939 (1982)
Cardelli, L., Zavattaro, G.: Turing universality of the biochemical ground form. Math. Struct. Comp. Sci. 20(1), 45–73 (2010)
Soloveichik, D., Cook, M., Winfree, E., Bruck, J.: Computation with finite stochastic chemical reaction networks. Nat. Comput. 7, 615–633 (2008)
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)
Jiang, H., Riedel, M.D., Parhi, K.K.: Synchronous sequential computation with molecular reactions. In: Design Automation Conference, San Diego, California, USA, June 5–10 (2011)
Rothemund, P.W.K.: A DNA and restriction enzyme implementation of Turing machines. In: Lipton, R.J., Baum, E.B. (eds.) DNA Based Computers: DIMACS Workshop, held April 4, pp. 75–120. American Mathematical Society, Providence (1996)
Kupferman, O., Vardi, M.Y.: An automata-theoretic approach to modular model checking. ACM T. Progr. Lang. Sys. 22(1), 87–128 (2000)
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
Lakin, M.R., Phillips, A. (2011). Modelling, Simulating and Verifying Turing-Powerful Strand Displacement Systems. In: Cardelli, L., Shih, W. (eds) DNA Computing and Molecular Programming. DNA 2011. Lecture Notes in Computer Science, vol 6937. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23638-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-23638-9_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23637-2
Online ISBN: 978-3-642-23638-9
eBook Packages: Computer ScienceComputer Science (R0)