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Chemical Reaction Networks and Stochastic Local Search

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DNA Computing and Molecular Programming (DNA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11648))

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Abstract

Stochastic local search can be an effective method for solving a wide variety of optimization and constraint satisfaction problems. Here I show that some stochastic local search algorithms map naturally to stochastic chemical reaction networks. This connection highlights new ways in which stochasticity in chemical reaction networks can be used for search and thus for finding solutions to problems. The central example is a chemical reaction network construction for solving Boolean formula satisfiability problems. Using an efficient general-purpose stochastic chemical reaction network simulator, I show that direct simulation of the networks proposed here can be more efficient, in wall-clock time, than a somewhat outdated but industrial-strength commercial satisfiability solver. While not of use for practical computing, the constructions emphasize that exploiting the stochasticity inherent in chemical reaction network dynamics is not inherently inefficient – and indeed I propose that stochastic local search could be an important aspect of biological computation and should be exploited when engineering future artificial cells.

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Notes

  1. 1.

    The sequence of reactions identified in the proof will have a positive probability of occurring next, specifically, at least \((12M+L)^{-(N+M)}\). This provides an exponential bound on the expected time to halt, to wit, less than \((12M+L)^{N+M}/k+(N+M)/k\). But is that useful?

  2. 2.

    A straightforward adaptation of the previous argument works for a closely related CRN that is identical to WalkSATCRN[f] except that species tryX0 and tryX1 are conflated as tryX for each variable X. This CRN should work similarly, as the main difference is merely that a variable being flipped now might spontaneously revert. But it is not the CRN that I simulated.

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Acknowledgements

This work was supported in part by National Science Foundation (NSF) grant 1317694 – The Molecular Programming Project. Thanks to Matt Cook, David Soloveichik, Chris Thachuk, William Poole, Lulu Qian, Grzegorz Rozenberg, Moshe Vardi, Tony Rojko, and Henry Lester for stimulating questions, comments, and encouragement.

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  1. California Institute of Technology, Pasadena, CA, USA

    Erik Winfree

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  1. California Institute of Technology, Pasadena, CA, USA

    Chris Thachuk

  2. Arizona State University, Tempe, AZ, USA

    Yan Liu

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Winfree, E. (2019). Chemical Reaction Networks and Stochastic Local Search. In: Thachuk, C., Liu, Y. (eds) DNA Computing and Molecular Programming. DNA 2019. Lecture Notes in Computer Science(), vol 11648. Springer, Cham. https://doi.org/10.1007/978-3-030-26807-7_1

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