Reachability and the Power of Local Ordering

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Reachability and the Power of Local Ordering
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 rst-order logic augmented with the appropriate Transitive Closure operator I87]: (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) GM92]. An apparently quite di erent \structured" model of logspace machines is the Jumping Automaton on Graphs (JAG), CR80]. 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 de ne. Furthermore, the language (FO + DTC + 2LO) 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 uppe...
Kousha Etessami, Neil Immerman
Added 10 Aug 2010
Updated 10 Aug 2010
Type Conference
Year 1994
Authors Kousha Etessami, Neil Immerman
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