Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the longest common subsequence of Thue-Morse words   The length $a(n)$ of the longest common subsequence of the $n$'th Thue-Morse
word and its bitwise complement is studied. An open problem suggested by Jean
Berstel in 2006 is to find a formula for $a(n)$. In this paper we prove new
lower bounds on $a(n)$ by explicitly constructing a common subsequence between
the Thue-Morse words and their bitwise complement. We obtain the lower bound
$a(n) = 2^{n}(1-o(1))$, saying that when $n$ grows large, the fraction of
omitted symbols in the longest common subsequence of the $n$'th Thue-Morse word
and its bitwise complement goes to $0$. We further generalize to any prefix of
the Thue-Morse sequence, where we prove similar lower bounds.

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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
31
The categories of this paper are: ao-sci