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...

• Type: Conference
• Year: 1994
• Where: STACS
• Authors: Kousha Etessami, Neil Immerman
• Keywords: JAG Model, Major Unresolved Problems, STACS 1994, Theoretical Computer Science, Two-way Jag Model