Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The overlap gap between left-infinite and right-infinite words   Given two finite words $u$ and $v$ of equal length, define the \emph{overlap
gap between $u$ and $v$}, denoted $og(u,v)$, as the least integer $m$ for which
there exist words $x$ and $x'$ of length $m$ such that $xu=vx'$ or $ux=x'v$.
Informally, the overlap gap measures the outside parts of the greatest overlap
of the given words.
  For a left-infinite word $\lambda$ and a right-infinite word $\rho$, let
$og_{\lambda,\rho}$ be the function defined, for each non-negative integer $n$,
by $og_{\lambda,\rho}(n)=og(\lambda_n,\rho_n)$, where $\lambda_n$ and $\rho_n$
are, respectively, the suffix of $\lambda$ and the prefix of $\rho$ of length
$n$. Also, denote by $OG_{\lambda,\rho}$ the image of the function
$og_{\lambda,\rho}$.
  In this paper, we show that $OG_{\lambda,\rho}$ is a finite set if and only
if $\lambda$ and $\rho$ are ultimately periodic infinite words of the form
$\lambda=u^{-\infty}w_1=\cdots uuuw_1$ and $\rho=w_2u^\infty=w_2uuu\cdots$ for
some finite words $u$, $w_1$ and $w_2$.

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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat