All reports by Author Neil Immerman:

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TR07-008
| 27th November 2006
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Philipp Weis, Neil Immerman#### Structure Theorem and Strict Alternation Hierarchy for FO^2 on Words

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TR04-100
| 23rd November 2004
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Eric Allender, Michael Bauland, Neil Immerman, Henning Schnoor, Heribert Vollmer#### The Complexity of Satisfiability Problems: Refining Schaefer's Theorem

Revisions: 1

Philipp Weis, Neil Immerman

It is well-known that every first-order property on words is expressible

using at most three variables. The subclass of properties expressible with

only two variables is also quite interesting and well-studied. We prove

precise structure theorems that characterize the exact expressive power of

first-order logic with two variables on words. ...
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Eric Allender, Michael Bauland, Neil Immerman, Henning Schnoor, Heribert Vollmer

Schaefer proved in 1978 that the Boolean constraint satisfaction problem for a given constraint language is either in P or is NP-complete, and identified all tractable cases. Schaefer's dichotomy theorem actually shows that there are at most two constraint satisfaction problems, up to polynomial-time isomorphism (and these isomorphism types are ... more >>>