@InProceedings{weis_et_al:DagSemProc.06451.6, author = {Weis, Philipp and Immerman, Neil}, title = {{Structure Theorem and Strict Alternation Hierarchy for FO\~{A}‚\^{A}² on Words}}, booktitle = {Circuits, Logic, and Games}, pages = {1--22}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2007}, volume = {6451}, editor = {Thomas Schwentick and Denis Th\'{e}rien and Heribert Vollmer}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06451.6}, URN = {urn:nbn:de:0030-drops-9751}, doi = {10.4230/DagSemProc.06451.6}, annote = {Keywords: Descriptive complexity, finite model theory, alternation hierarchy, Ehrenfeucht-Fraisse games} }