Real-time computability of real numbers by chemical reaction networks View Full Text


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Article Info

DATE

2019-03

AUTHORS

Xiang Huang, Titus H. Klinge, James I. Lathrop, Xiaoyuan Li, Jack H. Lutz

ABSTRACT

We explore the class of real numbers that are computed in real time by deterministic chemical reaction networks that are integral in the sense that all their reaction rate constants are positive integers. We say that such a reaction network computes a real number α in real time if it has a designated species X such that, when all species concentrations are set to zero at time t=0, the concentration x(t) of X is within 2-t of |α| at all times t≥1, and the concentrations of all other species are bounded. We show that every algebraic number and some transcendental numbers are real time computable by chemical reaction networks in this sense. We discuss possible implications of this for the 1965 Hartmanis–Stearns conjecture, which says that no irrational algebraic number is real time computable by a Turing machine. More... »

PAGES

63-73

References to SciGraph publications

  • 1989. Nearly linear time in LOGIC AT BOTIK '89
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  • 2000. Computable Analysis, An Introduction in NONE
  • 2009. Programmability of Chemical Reaction Networks in ALGORITHMIC BIOPROCESSES
  • 2017-09-01. Strong Turing Completeness of Continuous Chemical Reaction Networks and Compilation of Mixed Analog-Digital Programs in COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY
  • 2012. Computing with Large Populations Using Interactions in MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE 2012
  • 2013-10. Programmable chemical controllers made from DNA in NATURE NANOTECHNOLOGY
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    http://scigraph.springernature.com/pub.10.1007/s11047-018-9706-x

    DOI

    http://dx.doi.org/10.1007/s11047-018-9706-x

    DIMENSIONS

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