Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Practical KMP/BM Style Pattern-Matching on Indeterminate Strings   In this paper we describe two simple, fast, space-efficient algorithms for
finding all matches of an indeterminate pattern $p = p[1..m]$ in an
indeterminate string $x = x[1..n]$, where both $p$ and $x$ are defined on a
"small" ordered alphabet $\Sigma$ $-$ say, $\sigma = |\Sigma| \le 9$. Both
algorithms depend on a preprocessing phase that replaces $\Sigma$ by an integer
alphabet $\Sigma_I$ of size $\sigma_I = \sigma$ which (reversibly, in time
linear in string length) maps both $x$ and $p$ into equivalent regular strings
$y$ and $q$, respectively, on $\Sigma_I$, whose maximum (indeterminate) letter
can be expressed in a 32-bit word (for $\sigma \le 4$, thus for DNA sequences,
an 8-bit representation suffices). We first describe an efficient version KMP
Indet of the venerable Knuth-Morris-Pratt algorithm to find all occurrences of
$q$ in $y$ (that is, of $p$ in $x$), but, whenever necessary, using the prefix
array, rather than the border array, to control shifts of the transformed
pattern $q$ along the transformed string $y$. We go on to describe a similar
efficient version BM Indet of the Boyer- Moore algorithm that turns out to
execute significantly faster than KMP Indet over a wide range of test cases. A
noteworthy feature is that both algorithms require very little additional
space: $\Theta(m)$ words. We conjecture that a similar approach may yield
practical and efficient indeterminate equivalents to other well-known
pattern-matching algorithms, in particular the several variants of Boyer-Moore.

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The categories of this paper are: supr-con
16
The categories of this paper are: stat
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The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph