On the Power of Unambiguity in Logspace

Aduri Pavan; Raghunath Tewari; N. V. Vinodchandran

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arXiv · 1001.2034

On the Power of Unambiguity in Logspace

Aduri Pavan·Raghunath Tewari·N. V. Vinodchandran

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Abstract

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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BibTeX RIS

Aduri Pavan, Raghunath Tewari, N. V. Vinodchandran. 2010-01-12. On the Power of Unambiguity in Logspace. https://arxiv.org/abs/1001.2034

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