Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Affine Reachability Problems   We analyze affine reachability problems in dimensions 1 and 2. We show that
the reachability problem for 1-register machines over the integers with affine
updates is PSPACE-hard, hence PSPACE-complete, strengthening a result by Finkel
et al. that required polynomial updates. Building on recent results on
two-dimensional integer matrices, we prove NP-completeness of the mortality
problem for 2-dimensional integer matrices with determinants +1 and 0.
Motivated by tight connections with 1-dimensional affine reachability problems
without control states, we also study the complexity of a number of
reachability problems in finitely generated semigroups of 2-dimensional
upper-triangular integer matrices.

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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: solv-int
3
The categories of this paper are: physics
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The categories of this paper are: atom-ph