Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Containment Problem for Linear Sets   It is well known that the containment problem (as well as the equivalence
problem) for semilinear sets is $\log$-complete in $\Pi_2^p$. It had been shown
quite recently that already the containment problem for multi-dimensional
linear sets is $\log$-complete in $\Pi_2^p$ (where hardness even holds for a
unary encoding of the numerical input parameters). In this paper, we show that
already the containment problem for $1$-dimensional linear sets (with binary
encoding of the numerical input parameters) is $\log$-hard (and therefore also
$\log$-complete) in $\Pi_2^p$. However, combining both restrictions (dimension
$1$ and unary encoding), the problem becomes solvable in polynomial time.

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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: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph