Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computational Complexity of Atomic Chemical Reaction Networks   Informally, a chemical reaction network is "atomic" if each reaction may be
interpreted as the rearrangement of indivisible units of matter. There are
several reasonable definitions formalizing this idea. We investigate the
computational complexity of deciding whether a given network is atomic
according to each of these definitions.
  Our first definition, primitive atomic, which requires each reaction to
preserve the total number of atoms, is to shown to be equivalent to mass
conservation. Since it is known that it can be decided in polynomial time
whether a given chemical reaction network is mass-conserving, the equivalence
gives an efficient algorithm to decide primitive atomicity.
  Another definition, subset atomic, further requires that all atoms are
species. We show that deciding whether a given network is subset atomic is in
$\textsf{NP}$, and the problem "is a network subset atomic with respect to a
given atom set" is strongly $\textsf{NP}$-$\textsf{Complete}$.
  A third definition, reachably atomic, studied by Adleman, Gopalkrishnan et
al., further requires that each species has a sequence of reactions splitting
it into its constituent atoms. We show that there is a $\textbf{polynomial-time
algorithm}$ to decide whether a given network is reachably atomic, improving
upon the result of Adleman et al. that the problem is $\textbf{decidable}$. We
show that the reachability problem for reachably atomic networks is
$\textsf{Pspace}$-$\textsf{Complete}$.
  Finally, we demonstrate equivalence relationships between our definitions and
some special cases of another existing definition of atomicity due to Gnacadja.

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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: alg-geom