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- W2091276604 abstract "The L NL question remains one of the major unresolved problems in complexity theory. Both L and NL have logical characterizations as the sets of totally ordered (⩽) structures expressible in first-order logic augmented with the appropriate Transitive Closure operator (Immerman, 1987): ( FO + DTC + ⩽) captures L and ( FO + TC + ⩽) captures NL. On the other hand, in the absence of ordering, ( FO + TC ) is strictly more powerful than ( FO + DTC ) (Grädel and McColm, 1992). An apparently quite different “structured” model of logspace machines is the Jumping Automaton on Graphs (JAG), (Cook and Rockoff, 1980). We show that the JAG model is intimately related to these logics on “one-way locally ordered” (1LO) structures. We argue that the usual JAG model is unreasonably weak and should be replaced, wherever possible, by the two-way JAG model, which we define. Furthermore, the language ( FO + DTC + 2 LO ) over two-way locally ordered (2LO) graphs is more robust than even the two-way JAG model, and yet lower bounds remain accessible. We prove an upper bound on the power of TC over one-way locally ordered graphs, and three lower bounds on DTC." @default.
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- W2091276604 date "1995-09-01" @default.
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- W2091276604 title "Reachability and the power of local ordering" @default.
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- W2091276604 doi "https://doi.org/10.1016/0304-3975(95)00034-t" @default.
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