Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Power of Unambiguity in Logspace   We report progress on the \NL vs \UL problem. [-] We show unconditionally
that the complexity class $\ReachFewL\subseteq\UL$. This improves on the
earlier known upper bound $\ReachFewL \subseteq \FewL$. [-] We investigate the
complexity of min-uniqueness - a central notion in studying the \NL vs \UL
problem. We show that min-uniqueness is necessary and sufficient for showing
$\NL =\UL$. We revisit the class $\OptL[\log n]$ and show that {\sc
ShortestPathLength} - computing the length of the shortest path in a DAG, is
complete for $\OptL[\log n]$. We introduce $\UOptL[\log n]$, an unambiguous
version of $\OptL[\log n]$, and show that (a) $\NL =\UL$ if and only if
$\OptL[\log n] = \UOptL[\log n]$, (b) $\LogFew \leq \UOptL[\log n] \leq \SPL$.
[-] We show that the reachability problem over graphs embedded on 3 pages is
complete for \NL. This contrasts with the reachability problem over graphs
embedded on 2 pages which is logspace equivalent to the reachability problem in
planar graphs and hence is in \UL.

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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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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: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol