Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Matching Patterns with Variables under Hamming Distance   A pattern $\alpha$ is a string of variables and terminal letters. We say that
$\alpha$ matches a word $w$, consisting only of terminal letters, if $w$ can be
obtained by replacing the variables of $\alpha$ by terminal words. The matching
problem, i.e., deciding whether a given pattern matches a given word, was
heavily investigated: it is NP-complete in general, but can be solved
efficiently for classes of patterns with restricted structure. In this paper,
we approach this problem in a generalized setting, by considering approximate
pattern matching under Hamming distance. More precisely, we are interested in
what is the minimum Hamming distance between $w$ and any word $u$ obtained by
replacing the variables of $\alpha$ by terminal words. Firstly, we address the
class of regular patterns (in which no variable occurs twice) and propose
efficient algorithms for this problem, as well as matching conditional lower
bounds. We show that the problem can still be solved efficiently if we allow
repeated variables, but restrict the way the different variables can be
interleaved according to a locality parameter. However, as soon as we allow a
variable to occur more than once and its occurrences can be interleaved
arbitrarily with those of other variables, even if none of them occurs more
than once, the problem becomes intractable.

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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: math
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph