{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:18:47Z","timestamp":1759637927797},"publisher-location":"Berlin, Heidelberg","reference-count":21,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540749141"},{"type":"electronic","value":"9783540749158"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-3-540-74915-8_27","type":"book-chapter","created":{"date-parts":[[2007,8,24]],"date-time":"2007-08-24T05:13:35Z","timestamp":1187932415000},"page":"343-357","source":"Crossref","is-referenced-by-count":6,"title":["Structure Theorem and Strict Alternation Hierarchy for FO2 on Words"],"prefix":"10.1007","author":[{"given":"P.","family":"Weis","sequence":"first","affiliation":[]},{"given":"N.","family":"Immerman","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"issue":"3","key":"27_CR1","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1145\/772062.772064","volume":"4","author":"M. Adler","year":"2003","unstructured":"Adler, M., Immerman, N.: An n! lower bound on formula size. ACM Transactions on Computational Logic\u00a04(3), 296\u2013314 (2003)","journal-title":"ACM Transactions on Computational Logic"},{"key":"27_CR2","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/0022-0000(78)90049-1","volume":"16","author":"J. Brzozowski","year":"1978","unstructured":"Brzozowski, J., Knast, R.: The dot-depth hierarchy of star-free languages is infinite. Journal of Computer and System Science\u00a016, 37\u201355 (1978)","journal-title":"Journal of Computer and System Science"},{"key":"27_CR3","doi-asserted-by":"crossref","unstructured":"Etessami, K., Vardi, M.Y., Wilke, T.: First-order logic with two variables and unary temporal logic. In: IEEE Symposium on Logic in Computer Science (1997)","DOI":"10.1109\/LICS.1997.614950"},{"issue":"2","key":"27_CR4","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1006\/inco.2001.2953","volume":"179","author":"K. Etessami","year":"2002","unstructured":"Etessami, K., Vardi, M.Y., Wilke, T.: First-order logic with two variables and unary temporal logic. Information and Computation\u00a0179(2), 279\u2013295 (2002)","journal-title":"Information and Computation"},{"key":"27_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2168\/LMCS-1(1:6)2005","volume":"1","author":"M. Grohe","year":"2005","unstructured":"Grohe, M., Schweikardt, N.: The succinctness of first-order logic on linear orders. Logical Methods in Computer Science\u00a01, 1\u20136 (2005)","journal-title":"Logical Methods in Computer Science"},{"key":"27_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0539-5","volume-title":"Descriptive complexity","author":"N. Immerman","year":"1999","unstructured":"Immerman, N.: Descriptive complexity. Springer, Heidelberg (1999)"},{"issue":"2","key":"27_CR7","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1016\/0890-5401(89)90055-2","volume":"83","author":"N. Immerman","year":"1989","unstructured":"Immerman, N., Kozen, D.: Definability with bounded number of bound variables. Information and Computation\u00a083(2), 121\u2013139 (1989)","journal-title":"Information and Computation"},{"key":"27_CR8","unstructured":"Kamp, J.A.: Tense logic and the theory of linear order. PhD thesis, University of California, Los Angeles (1968)"},{"issue":"2","key":"27_CR9","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1137\/0403021","volume":"3","author":"M. Karchmer","year":"1990","unstructured":"Karchmer, M., Wigderson, A.: Monotone circuits for connectivity require super-logarithmic depth. SIAM Journal of Discrete Mathematics\u00a03(2), 255\u2013265 (1990)","journal-title":"SIAM Journal of Discrete Mathematics"},{"key":"27_CR10","volume-title":"Counter-free automata","author":"R. McNaughton","year":"1971","unstructured":"McNaughton, R., Papert, S.A.: Counter-free automata. MIT Press, Cambridge (1971)"},{"key":"27_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF02679450","volume":"30","author":"J.-E. Pin","year":"1997","unstructured":"Pin, J.-E., Weil, P.: Polynomial closure and unambiguous product. Theory of Computing Systems\u00a030, 1\u201339 (1997)","journal-title":"Theory of Computing Systems"},{"key":"27_CR12","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/BF02194921","volume":"13","author":"M.P. Sch\u00fctzenberger","year":"1976","unstructured":"Sch\u00fctzenberger, M.P.: Sur le produit de concatenation non ambigu. Semigroup Forum\u00a013, 47\u201375 (1976)","journal-title":"Semigroup Forum"},{"key":"27_CR13","doi-asserted-by":"crossref","unstructured":"Schwentick, T., Th\u00e9rien, D., Vollmer, H.: Partially-ordered two-way automata: a new characterization of DA. In Developments in Language Theory (2001)","DOI":"10.1007\/3-540-46011-X_20"},{"key":"27_CR14","doi-asserted-by":"crossref","unstructured":"Straubing, H., Th\u00e9rien, D.: Weakly iterated block products. In: 5th Latin American Theoretical Informatics Conference (2002)","DOI":"10.1007\/3-540-45995-2_13"},{"key":"27_CR15","doi-asserted-by":"crossref","unstructured":"Tesson, P., Th\u00e9rien, D.: Diamonds are forever: the variety DA. In Semigroups, Algorithms, Automata and Languages (2001)","DOI":"10.1142\/9789812776884_0021"},{"key":"27_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2168\/LMCS-3(1:4)2007","volume":"3","author":"P. Tesson","year":"2007","unstructured":"Tesson, P., Th\u00e9rien, D.: Algebra meets logic: the case of regular languages. Logical Methods in Computer Science\u00a03, 1\u20134 (2007)","journal-title":"Logical Methods in Computer Science"},{"key":"27_CR17","doi-asserted-by":"crossref","unstructured":"Th\u00e9rien, D., Wilke, T.: Over words, two variables are as powerful as one quantifier alternation. In: ACM Symposium on Theory of Computing (1998)","DOI":"10.1145\/276698.276749"},{"key":"27_CR18","doi-asserted-by":"publisher","first-page":"360","DOI":"10.1016\/0022-0000(82)90016-2","volume":"25","author":"W. Thomas","year":"1982","unstructured":"Thomas, W.: Classifying regular events in symbolic logic. Journal of Computer and System Science\u00a025, 360\u2013376 (1982)","journal-title":"Journal of Computer and System Science"},{"key":"27_CR19","doi-asserted-by":"crossref","first-page":"11","DOI":"10.24033\/msmf.309","volume":"16","author":"W. Thomas","year":"1984","unstructured":"Thomas, W.: An application of the Ehrenfeucht-Fra\u00efss\u00e9 game in formal language theory. M\u00e9moires de la S.M.F\u00a016, 11\u201321 (1984)","journal-title":"M\u00e9moires de la S.M.F"},{"key":"27_CR20","unstructured":"Weis, P., and Immerman, N.: Structure theorem and strict alternation hierarchy for FO2 on words (2007), http:\/\/www.cs.umass.edu\/~immerman\/pub\/FO2_on_words.pdf"},{"key":"27_CR21","unstructured":"Wilke, T.: Personal communication (2007)"}],"container-title":["Lecture Notes in Computer Science","Computer Science Logic"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-74915-8_27.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T10:45:50Z","timestamp":1619520350000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-74915-8_27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540749141","9783540749158"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-74915-8_27","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[]}}