On the Power of Unambiguity in Logspace
Aduri Pavan, Raghunath Tewari, N. V. Vinodchandran

TL;DR
This paper advances understanding of the NL vs UL complexity classes by establishing new inclusions, exploring min-uniqueness, and introducing unambiguous variants of OptL, with implications for graph reachability problems.
Contribution
It proves that ReachFewL is contained in UL, explores the role of min-uniqueness in NL=UL, and introduces UOptL[log n] as an unambiguous class related to OptL[log n].
Findings
ReachFewL UL unconditionally.
Min-uniqueness is necessary and sufficient for NL=UL.
Reachability on 3-page graphs is NL-complete.
Abstract
We report progress on the \NL vs \UL problem. [-] We show unconditionally that the complexity class . This improves on the earlier known upper bound . [-] 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 . We revisit the class and show that {\sc ShortestPathLength} - computing the length of the shortest path in a DAG, is complete for . We introduce , an unambiguous version of , and show that (a) if and only if , (b) . [-] We show that the reachability problem over graphs embedded on 3 pages is complete for \NL. This contrasts with the reachability problem over…
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · semigroups and automata theory
