Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Real-Time Computability of Real Numbers by Chemical Reaction Networks   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 $\alpha$ 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
$|{\alpha}|$ at all times $t \ge 1$, 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.

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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
2
The categories of this paper are: math
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci